Finite Group Databasebeta

← #13172739

Subgroups — #13172739

Order 1728.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#88953C211yesmaximal, characteristic, complemented
3#11723634C211yesmaximal, characteristic, complemented
4#11723631C211yesmaximal, characteristic, complemented
5#11723621C211yesmaximal, characteristic, complemented
6C3×#63983C211yesmaximal, characteristic, complemented
7C3×#63981C211yesmaximal, characteristic, complemented
8C3×#63958C211yesmaximal, characteristic, complemented
9#11722998C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722994C211yesmaximal, characteristic, complemented
12#11722967C211yesmaximal, characteristic, complemented
13#11722957C211yesmaximal, characteristic, complemented
14#11722947C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595281—31nomaximal
17#10595280—31nomaximal
18#10594263—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic, complemented
20C22×#1113C2211yescharacteristic
21C22×C3×D32C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26#89049—24no—
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic, complemented
29C2×#6294C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic, complemented
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic
36C2×C3×#626C2211yescharacteristic, complemented
37C2×C3×#626C2211yescharacteristic, complemented
38C2×C3×#624C2211yescharacteristic, complemented
39#88953—24no—
40#88864C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×D3×#67—31no—
61C2×#3802—31no—
62#64147—31no—
63#64146—31no—
64#64092—31no—
65C3×#938—31no—
66C3×#937—31no—
67C3×#937—31no—
68C3×#937—31no—
69C3×#884—31no—
70C3×#882—31no—
71#63983D311yescharacteristic, complemented
72#63981D311yescharacteristic, complemented
73#63977—31no—
74#63976—31no—
75#63976—31no—
76#63976—31no—
77#63976—61no—
78#63975—31no—
79#63971—31no—
80#63970—31no—
81#63970—31no—
82#63970—61no—
83#63969—31no—
84#63969—31no—
85#63969—31no—
86#63969—61no—
87#63958—31no—
88#63958D311yescharacteristic, complemented
89#63922—31no—
90#63921—31no—
91D3×(C2×D3)⋊C4—31no—
92D3×(C2×D3)⋊C4—31no—
93#63912—31no—
94#63908—31no—
95#63906—31no—
96#63891—31no—
97#63891—31no—
98#63891—31no—
99#63890—31no—
100#63885—31no—
101#63884—31no—
102#63854—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C22×C32×D3C2311yescharacteristic
114C2×#1113—41no—
115C2×#1113—41no—
116C2×#1113D414yescomplemented
117C2×C3×D32—22no—
118C2×C3×D32—41no—
119C2×C3×D32—41no—
120C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
121C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
122C3×#638—22no—
123C3×#638—22no—
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C32×#67—41no—
127C32×#67—41no—
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131C2×C32×Dic3C2311yescharacteristic
132#6295—22no—
133#6295—22no—
134#6294—22no—
135#6290—22no—
136#6290—22no—
137#6290—41no—
138Dic3×C3⋊D3—22no—
139Dic3×C3⋊D3—41no—
140C3×#626—22no—
141C3×#626—22no—
142C3×#626—41no—
143C3×#624—41no—
144#5605—91no—
145#5589—91no—
146#5589—91no—
147C23×C3⋊D3C2×D311yescharacteristic, complemented
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3—31no—
151C23×C3×D3—31no—
152C23×C3×D3—61no—
153C22×D32—31no—
154C22×D32—31no—
155C22×D32—31no—
156C22×D32C2×D311yescharacteristic, complemented
157C2×C32×D4—31no—
158C2×C32×D4—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638C2×D311yescharacteristic
163C2×#638C2×D311yescharacteristic, complemented
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—21no—
167C2×C3×#67—21no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—61no—
176C2×C3×#67—61no—
177C2×C3×#67C2×D311yescharacteristic, complemented
178C2×C3×#67C2×D311yescharacteristic, complemented
179C2×C3×#67C2×D311yescharacteristic, complemented
180C2×C3×#67C2×D311yescharacteristic, complemented
181C2×C3×D12—31no—
182C2×C3×D12—31no—
183C2×C3×D12—31no—
184C2×C3×C4×D3—31no—
185C2×C3×C4×D3—31no—
186#3811—64no—
187D3×#67—64no—
188D3×#67—64no—
189D3×#67—64no—
190D3×#67—64no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626C2×D311yescharacteristic
196C2×#626C2×D311yescharacteristic, complemented
197C2×#626C2×D311yescharacteristic, complemented
198C2×#625—31no—
199C2×#625—31no—
200C2×#625—31no—
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—31no—
204C2×#625—31no—
205C2×#625—31no—
206C2×#625—61no—
207C2×#625—61no—
208C2×#625—61no—
209C2×#624—31no—
210C2×#624C2×D311yescharacteristic, complemented
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—61no—
218C2×D3×Dic3—61no—
219#3802—64no—
220C32×C22⋊C4—31no—
221#3757—31no—
222#3757—31no—
223#3757—31no—
224#3757—31no—
225#3757—61no—
226#3757—61no—
227#3757—61no—
228#3757—121no—
229#3752—31no—
230#3752—31no—
231#3752—31no—
232C4⋊(C3⋊Dic3)—31no—
233C4⋊(C3⋊Dic3)—31no—
234#3750—31no—
235C3×#217—21no—
236C3×#217—31no—
237C3×#217—31no—
238C3×#217—31no—
239C3×#217C2×D311yescharacteristic, complemented
240C3×#217C2×D311yescharacteristic, complemented
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×(C2×D3)⋊C4—31no—
247C3×(C2×D3)⋊C4—31no—
248C3×(C2×D3)⋊C4—31no—
249C3×(C2×D3)⋊C4—31no—
250C3×C4⋊Dic3—31no—
251C3×Dic3⋊C4—31no—
252#3724—31no—
253#3724—31no—
254#3724—61no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—31no—
259Dic3⋊Dic3—61no—
260Dic3⋊Dic3—61no—
261Dic3⋊Dic3C2×D311yescharacteristic, complemented
262#3722C2×D311yescharacteristic, complemented
263#3722C2×D311yescharacteristic, complemented
264#3722C2×D311yescharacteristic, complemented
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3—61no—
276(C2×D3)⋊Dic3—61no—
277(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
278(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
279(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2411yescharacteristic
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—44no—
294C2×C3×C3⋊D3C2×D412yes—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C3×C3⋊D3C2×D412yes—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C2×C32×D3—21no—
300C2×C32×D3—21no—
301C2×C32×D3—21no—
302C2×C32×D3—21no—
303#1113—44no—
304C3×D32—44no—
305C3⋊(C3⋊Dic3)—21no—
306C3⋊(C3⋊Dic3)—21no—
307C3×C3⋊Dic3—21no—
308C3×C3⋊Dic3—21no—
309C32×Dic3—21no—
310C32×Dic3—21no—
311C32×Dic3—21no—
312C32×Dic3—21no—
313C22×#67—91no—
314C22×#67—91no—
315C2×D3×D4—91no—
316C2×D3×D4—91no—
317C2×D3×D4—91no—
318C2×D3×D4—91no—
319C3×#121—91no—
320C3×#120—91no—
321C3×#120—91no—
322#953—91no—
323#953—91no—
324#939—91no—
325#939—91no—
326#938—31no—
327#938—91no—
328#938—91no—
329#938—91no—
330#938—181no—
331#937—31no—
332#937—31no—
333#937—31no—
334#937—91no—
335#937—91no—
336#937—91no—
337#937—181no—
338#935—91no—
339#935—91no—
340#930—91no—
341C2×(C2×D3)⋊C4—91no—
342#894—91no—
343#894—91no—
344#886—91no—
345#886—91no—
346#884—31no—
347#884—91no—
348#884—91no—
349#884—91no—
350#883—91no—
351#883—91no—
352#883—91no—
353#883—91no—
354#883—91no—
355#883—91no—
356#883—181no—
357#882—31no—
358#882—91no—
359D3×C22⋊C4—91no—
360D3×C22⋊C4—91no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—21no—
364C23×C32—31no—
365C23×C32—31no—
366C23×C32—41no—
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C23×C32C22×D311yescharacteristic
370C22×C3⋊D3—22no—
371C22×C3⋊D3—41no—
372C22×C3⋊D3—41no—
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3×D3—21no—
378C22×C3×D3—21no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—61no—
388C22×C3×D3—61no—
389C22×C3×D3—61no—
390C22×C3×D3—61no—
391C22×C3×D3—62no—
392C22×C3×D3—62no—
393C22×C3×D3—62no—
394C22×C3×D3—62no—
395C22×C3×D3—122no—
396C22×C3×D3—121no—
397C22×C3×D3—121no—
398C22×C3×D3—121no—
399C22×C3×D3—121no—
400C22×C3×D3—121no—
401C22×C3×D3—121no—
402C22×C3×D3—121no—
403C22×C3×D3—121no—
404C22×C3×D3—122no—
405C22×C3×D3—122no—
406C22×C3×D3C22×D311yescharacteristic
407C22×C3×D3C22×D311yescharacteristic
408C22×C3×D3C22×D311yescharacteristic
409C22×C3×D3C22×D311yescharacteristic
410C2×D32—22no—
411C2×D32—34no—
412C2×D32—34no—
413C2×D32—34no—
414C2×D32—41no—
415C2×D32—41no—
416C2×D32—121no—
417C2×D32—121no—
418C2×D32—121no—
419C2×D32—121no—
420C2×D32—121no—
421C2×D32—121no—
422C32×D4—121no—
423C32×D4—121no—
424C2×C32×C4—31no—
425C2×C32×C4—31no—
426C2×C32×C4—31no—
427C2×C32×C4—31no—
428#638—22no—
429#638—22no—
430#638—62no—
431#638—62no—
432#638—121no—
433C2×C3⋊Dic3—31no—
434C2×C3⋊Dic3—31no—
435C2×C3⋊Dic3—31no—
436C2×C3⋊Dic3—31no—
437C2×C3⋊Dic3—31no—
438C2×C3⋊Dic3—31no—
439C2×C3⋊Dic3—61no—
440C2×C3⋊Dic3—61no—
441C2×C3⋊Dic3—61no—
442C2×C3⋊Dic3—61no—
443C2×C3⋊Dic3—61no—
444C2×C3⋊Dic3—61no—
445C2×C3⋊Dic3—121no—
446C2×C3⋊Dic3—121no—
447C2×C3⋊Dic3C22×D311yescharacteristic
448C2×C3⋊Dic3C22×D311yescharacteristic
449C4×C3⋊D3—62no—
450C4×C3⋊D3—121no—
451C3×#67—41no—
452C3×#67—41no—
453C3×#67—41no—
454C3×#67—41no—
455C3×#67—42no—
456C3×#67—42no—
457C3×#67—62no—
458C3×#67—62no—
459C3×#67—62no—
460C3×#67—62no—
461C3×#67—62no—
462C3×#67—62no—
463C3×#67—122no—
464C3×#67—122no—
465C3×#67—121no—
466C2×C3×Dic3—21no—
467C2×C3×Dic3—21no—
468C2×C3×Dic3—21no—
469C2×C3×Dic3—21no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—31no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—61no—
475C2×C3×Dic3—61no—
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C2×C3×Dic3C22×D311yescharacteristic
483C2×C3×Dic3C22×D311yescharacteristic
484C3×D12—62no—
485C3×D12—62no—
486C3×D12—121no—
487C3×C4×D3—121no—
488C3×C4×D3—121no—
489#626—22no—
490#626—22no—
491#626—41no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—62no—
496#625—62no—
497#625—62no—
498#625—62no—
499#625—62no—
500#625—62no—
501#625—62no—
502#625—122no—
503#625—122no—
504#625—121no—
505#625—121no—
506#625—122no—
507#624—41no—
508#624—62no—
509D3×Dic3—62no—
510D3×Dic3—62no—
511D3×Dic3—62no—
512D3×Dic3—62no—
513D3×Dic3—122no—
514D3×Dic3—121no—
515D3×Dic3—121no—
516D3×Dic3—122no—
517#534—271noSylow
518C2×C33—41no—
519C2×C33C22×D411yescharacteristic
520C2×C33H(5,𝔽2)11yescharacteristic
521C2×C33H(5,𝔽2)11yescharacteristic
522C3×C3⋊D3—22no—
523C3×C3⋊D3—22no—
524C3×C3⋊D3—22no—
525C3×C3⋊D3—41no—
526C32×D3—41no—
527C32×D3—41no—
528C24×C3—91no—
529C24×C3—91no—
530C23×D3—31no—
531C23×D3—31no—
532C23×D3—31no—
533C23×D3—31no—
534C23×D3—61no—
535C23×D3—91no—
536C23×D3—91no—
537C23×D3—91no—
538C2×C3×D4—31no—
539C2×C3×D4—31no—
540C2×C3×D4—31no—
541C2×C3×D4—31no—
542C2×C3×D4—61no—
543C2×C3×D4—61no—
544C2×C3×D4—91no—
545C2×C3×D4—91no—
546C2×C3×D4—91no—
547C2×C3×D4—91no—
548C2×C3×D4—91no—
549C22×C3×C4—91no—
550C2×#67—31no—
551C2×#67—31no—
552C2×#67—31no—
553C2×#67—31no—
554C2×#67—31no—
555C2×#67—31no—
556C2×#67—31no—
557C2×#67—61no—
558C2×#67—61no—
559C2×#67—91no—
560C2×#67—91no—
561C2×#67—91no—
562C2×#67—91no—
563C2×#67—91no—
564C2×#67—91no—
565C2×#67—91no—
566C2×#67—91no—
567C2×#67—91no—
568C2×#67—91no—
569C2×#67—91no—
570C2×#67—91no—
571C2×#67—91no—
572C2×#67—181no—
573C2×#67—181no—
574C2×#67—181no—
575C2×#67—184no—
576C2×#67—184no—
577C2×#67D3211yescharacteristic, complemented
578C2×#67D3211yescharacteristic, complemented
579C22×Dic3—91no—
580C22×Dic3—91no—
581C22×Dic3—91no—
582D3×D4—184no—
583D3×D4—184no—
584D3×D4—184no—
585D3×D4—184no—
586C2×D12—31no—
587C2×D12—31no—
588C2×D12—31no—
589C2×D12—91no—
590C2×D12—91no—
591C2×C4×D3—31no—
592C2×C4×D3—31no—
593C2×C4×D3—91no—
594C2×C4×D3—91no—
595C2×C4×D3—91no—
596C2×C4×D3—91no—
597C2×C4×D3—91no—
598C2×C4×D3—91no—
599C2×C4×D3—181no—
600C2×C4×D3—181no—
601C3×C4⋊C4—91no—
602C3×C22⋊C4—31no—
603C3×C22⋊C4—31no—
604C3×C22⋊C4—61no—
605C3×C22⋊C4—91no—
606C3×C22⋊C4—91no—
607C3×C22⋊C4—91no—
608C3×C22⋊C4—91no—
609C3×C22⋊C4—91no—
610C3×C22⋊C4—91no—
611#217—31no—
612#217—31no—
613#217—31no—
614#217—91no—
615#217—91no—
616#217—91no—
617#217—91no—
618#217—91no—
619#217—91no—
620#217—91no—
621#217—91no—
622#217—181no—
623#217—181no—
624#217—181no—
625#217—181no—
626#217—361no—
627#217D3211yescharacteristic, complemented
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—31no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—31no—
633(C2×D3)⋊C4—31no—
634(C2×D3)⋊C4—31no—
635(C2×D3)⋊C4—31no—
636(C2×D3)⋊C4—31no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—181no—
645(C2×D3)⋊C4—181no—
646(C2×D3)⋊C4—181no—
647C4⋊Dic3—31no—
648C4⋊Dic3—91no—
649C4⋊Dic3—91no—
650C4⋊Dic3—91no—
651C4⋊Dic3—91no—
652C4⋊Dic3—181no—
653C4⋊Dic3—181no—
654Dic3⋊C4—31no—
655Dic3⋊C4—91no—
656Dic3⋊C4—91no—
657Dic3⋊C4—91no—
658Dic3⋊C4—91no—
659Dic3⋊C4—91no—
660Dic3⋊C4—181no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—42no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—61no—
685C22×C32—61no—
686C22×C32—61no—
687C22×C32—61no—
688C22×C32—61no—
689C22×C32—61no—
690C22×C32—81no—
691C22×C32—81no—
692C22×C32C23×D311yescharacteristic
693C22×C32C23×D311yescharacteristic
694C22×C32C23×D311yescharacteristic
695C2×C3⋊D3—21no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C2×C3⋊D3—21no—
700C2×C3⋊D3—21no—
701C2×C3⋊D3—21no—
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—44no—
705C2×C3⋊D3D3×D412yes—
706C2×C3⋊D3D3×D412yes—
707C2×C3⋊D3D3×D412yes—
708C2×C3×D3—21no—
709C2×C3×D3—21no—
710C2×C3×D3—21no—
711C2×C3×D3—21no—
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—21no—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—32no—
721C2×C3×D3—32no—
722C2×C3×D3—32no—
723C2×C3×D3—32no—
724C2×C3×D3—32no—
725C2×C3×D3—32no—
726C2×C3×D3—41no—
727C2×C3×D3—41no—
728C2×C3×D3—41no—
729C2×C3×D3—41no—
730C2×C3×D3—41no—
731C2×C3×D3—41no—
732C2×C3×D3—62no—
733C2×C3×D3—62no—
734C2×C3×D3—62no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—62no—
748C2×C3×D3—61no—
749C2×C3×D3—61no—
750C2×C3×D3—61no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—61no—
754C2×C3×D3—121no—
755C2×C3×D3—121no—
756C2×C3×D3—121no—
757C2×C3×D3—121no—
758C2×C3×D3—121no—
759C2×C3×D3—121no—
760C2×C3×D3—121no—
761C2×C3×D3—121no—
762C2×C3×D3—124no—
763C2×C3×D3—124no—
764C2×C3×D3—124no—
765C2×C3×D3—124no—
766C2×C3×D3—128no—
767D32—44no—
768D32—124no—
769D32—124no—
770D32—124no—
771C32×C4—61no—
772C32×C4—61no—
773C32×C4—61no—
774C32×C4—61no—
775C3⋊Dic3—21no—
776C3⋊Dic3—21no—
777C3⋊Dic3—61no—
778C3⋊Dic3—61no—
779C3⋊Dic3—61no—
780C3⋊Dic3—61no—
781C3⋊Dic3—61no—
782C3⋊Dic3—61no—
783C3⋊Dic3—121no—
784C3⋊Dic3—121no—
785C3⋊Dic3—121no—
786C3⋊Dic3—121no—
787C3⋊Dic3—121no—
788C3⋊Dic3—121no—
789C3⋊Dic3—241no—
790C3⋊Dic3—241no—
791C3×Dic3—22no—
792C3×Dic3—21no—
793C3×Dic3—21no—
794C3×Dic3—21no—
795C3×Dic3—21no—
796C3×Dic3—21no—
797C3×Dic3—21no—
798C3×Dic3—21no—
799C3×Dic3—21no—
800C3×Dic3—41no—
801C3×Dic3—41no—
802C3×Dic3—41no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—121no—
808C3×Dic3—121no—
809C22×D4—271no—
810C22×D4—271no—
811#123—271no—
812#123—271no—
813#123—271no—
814#123—271no—
815#121—91no—
816#121—271no—
817#121—271no—
818#121—271no—
819#120—91no—
820#120—91no—
821#120—271no—
822#120—271no—
823C2×C22⋊C4—271no—
824C33#53411yescharacteristic, complemented, Sylow
825C23×C3—21no—
826C23×C3—21no—
827C23×C3—21no—
828C23×C3—31no—
829C23×C3—31no—
830C23×C3—31no—
831C23×C3—31no—
832C23×C3—41no—
833C23×C3—61no—
834C23×C3—61no—
835C23×C3—91no—
836C23×C3—91no—
837C23×C3—91no—
838C23×C3—91no—
839C23×C3—182no—
840C23×C3—182no—
841C23×C3—361no—
842C23×C3—361no—
843C23×C3—361no—
844C23×C3—361no—
845C23×C3C2×D3211yescharacteristic
846C23×C3C2×D3211yescharacteristic
847C23×C3C2×D3211yescharacteristic
848C22×D3—31no—
849C22×D3—31no—
850C22×D3—31no—
851C22×D3—31no—
852C22×D3—31no—
853C22×D3—31no—
854C22×D3—31no—
855C22×D3—31no—
856C22×D3—61no—
857C22×D3—61no—
858C22×D3—61no—
859C22×D3—61no—
860C22×D3—62no—
861C22×D3—62no—
862C22×D3—62no—
863C22×D3—62no—
864C22×D3—94no—
865C22×D3—94no—
866C22×D3—94no—
867C22×D3—122no—
868C22×D3—121no—
869C22×D3—121no—
870C22×D3—121no—
871C22×D3—121no—
872C22×D3—121no—
873C22×D3—121no—
874C22×D3—121no—
875C22×D3—121no—
876C22×D3—122no—
877C22×D3—122no—
878C22×D3—361no—
879C22×D3—361no—
880C22×D3—361no—
881C22×D3—361no—
882C22×D3—361no—
883C22×D3—361no—
884C22×D3C2×D3211yescharacteristic
885C22×D3C2×D3211yescharacteristic
886C3×D4—121no—
887C3×D4—121no—
888C3×D4—121no—
889C3×D4—121no—
890C3×D4—122no—
891C3×D4—122no—
892C3×D4—182no—
893C3×D4—182no—
894C3×D4—182no—
895C3×D4—182no—
896C3×D4—361no—
897C2×C3×C4—31no—
898C2×C3×C4—31no—
899C2×C3×C4—31no—
900C2×C3×C4—31no—
901C2×C3×C4—31no—
902C2×C3×C4—31no—
903C2×C3×C4—31no—
904C2×C3×C4—31no—
905C2×C3×C4—61no—
906C2×C3×C4—61no—
907C2×C3×C4—61no—
908C2×C3×C4—61no—
909C2×C3×C4—91no—
910C2×C3×C4—91no—
911C2×C3×C4—361no—
912#67—41no—
913#67—41no—
914#67—62no—
915#67—62no—
916#67—62no—
917#67—62no—
918#67—62no—
919#67—62no—
920#67—122no—
921#67—122no—
922#67—121no—
923#67—182no—
924#67—182no—
925#67—182no—
926#67—182no—
927#67—182no—
928#67—182no—
929#67—182no—
930#67—182no—
931#67—182no—
932#67—182no—
933#67—362no—
934#67—362no—
935#67—361no—
936#67—361no—
937#67—361no—
938#67—362no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—61no—
944C2×Dic3—61no—
945C2×Dic3—91no—
946C2×Dic3—91no—
947C2×Dic3—91no—
948C2×Dic3—91no—
949C2×Dic3—91no—
950C2×Dic3—91no—
951C2×Dic3—181no—
952C2×Dic3—181no—
953C2×Dic3—181no—
954C2×Dic3—181no—
955C2×Dic3—181no—
956C2×Dic3—181no—
957C2×Dic3—182no—
958C2×Dic3—182no—
959C2×Dic3—361no—
960C2×Dic3—361no—
961C2×Dic3—361no—
962C2×Dic3C2×D3211yescharacteristic
963C2×Dic3C2×D3211yescharacteristic
964C2×Dic3C2×D3211yescharacteristic
965C2×Dic3C2×D3211yescharacteristic
966D12—62no—
967D12—62no—
968D12—121no—
969D12—182no—
970D12—182no—
971C4×D3—121no—
972C4×D3—121no—
973C4×D3—182no—
974C4×D3—182no—
975C4×D3—182no—
976C4×D3—182no—
977C4×D3—362no—
978C4×D3—361no—
979C4×D3—361no—
980C4×D3—362no—
981C2×C32—21no—
982C2×C32—21no—
983C2×C32—21no—
984C2×C32—21no—
985C2×C32—21no—
986C2×C32—21no—
987C2×C32—21no—
988C2×C32—21no—
989C2×C32—21no—
990C2×C32—41no—
991C2×C32—41no—
992C2×C32—41no—
993C2×C32—41no—
994C2×C32—42no—
995C2×C32—41no—
996C2×C32—41no—
997C2×C32—81no—
998C2×C32—81no—
999C2×C32—82no—
1000C2×C32—121no—
1001C2×C32—121no—
1002C2×C32C2×D3×D411yescharacteristic
1003C2×C32C2×D3×D411yescharacteristic
1004C2×C32C2×D3×D411yescharacteristic
1005C2×C32#100411yescharacteristic
1006C2×C32#100411yescharacteristic
1007C2×C32#100411yescharacteristic
1008C2×C32#100411yescharacteristic
1009C2×C32#100411yescharacteristic
1010C2×C32#100911yescharacteristic
1011C3⋊D3—22no—
1012C3⋊D3—22no—
1013C3⋊D3—22no—
1014C3⋊D3—41no—
1015C3×D3—41no—
1016C3×D3—41no—
1017C3×D3—41no—
1018C3×D3—41no—
1019C3×D3—62no—
1020C3×D3—62no—
1021C3×D3—62no—
1022C3×D3—62no—
1023C3×D3—62no—
1024C3×D3—62no—
1025C3×D3—81no—
1026C3×D3—81no—
1027C3×D3—122no—
1028C3×D3—122no—
1029C3×D3—122no—
1030C3×D3—122no—
1031C3×D3—121no—
1032C3×D3—121no—
1033C24—91no—
1034C24—91no—
1035C24—271no—
1036C2×D4—31no—
1037C2×D4—31no—
1038C2×D4—91no—
1039C2×D4—91no—
1040C2×D4—91no—
1041C2×D4—91no—
1042C2×D4—91no—
1043C2×D4—271no—
1044C2×D4—271no—
1045C2×D4—271no—
1046C2×D4—271no—
1047C2×D4—271no—
1048C2×D4—544no—
1049C2×D4—544no—
1050C22×C4—91no—
1051C22×C4—271no—
1052C22×C4—271no—
1053C22×C4—271no—
1054C4⋊C4—91no—
1055C4⋊C4—271no—
1056C4⋊C4—271no—
1057C4⋊C4—271no—
1058C22⋊C4—31no—
1059C22⋊C4—91no—
1060C22⋊C4—91no—
1061C22⋊C4—91no—
1062C22⋊C4—91no—
1063C22⋊C4—91no—
1064C22⋊C4—91no—
1065C22⋊C4—271no—
1066C22⋊C4—271no—
1067C22⋊C4—271no—
1068C22⋊C4—271no—
1069C22⋊C4—271no—
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—21no—
1073C22×C3—21no—
1074C22×C3—21no—
1075C22×C3—21no—
1076C22×C3—21no—
1077C22×C3—21no—
1078C22×C3—21no—
1079C22×C3—21no—
1080C22×C3—21no—
1081C22×C3—21no—
1082C22×C3—21no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3—41no—
1086C22×C3—41no—
1087C22×C3—41no—
1088C22×C3—41no—
1089C22×C3—41no—
1090C22×C3—41no—
1091C22×C3—42no—
1092C22×C3—41no—
1093C22×C3—61no—
1094C22×C3—61no—
1095C22×C3—61no—
1096C22×C3—61no—
1097C22×C3—61no—
1098C22×C3—61no—
1099C22×C3—61no—
1100C22×C3—61no—
1101C22×C3—61no—
1102C22×C3—61no—
1103C22×C3—61no—
1104C22×C3—61no—
1105C22×C3—81no—
1106C22×C3—81no—
1107C22×C3—92no—
1108C22×C3—92no—
1109C22×C3—92no—
1110C22×C3—121no—
1111C22×C3—121no—
1112C22×C3—121no—
1113C22×C3—121no—
1114C22×C3—121no—
1115C22×C3—121no—
1116C22×C3—181no—
1117C22×C3—181no—
1118C22×C3—181no—
1119C22×C3—181no—
1120C22×C3—181no—
1121C22×C3—181no—
1122C22×C3—181no—
1123C22×C3—181no—
1124C22×C3—181no—
1125C22×C3—364no—
1126C22×C3—364no—
1127C22×C3C22×D3211yescharacteristic
1128C22×C3C22×D3211yescharacteristic
1129C22×C3C22×D3211yescharacteristic
1130C2×D3—21no—
1131C2×D3—21no—
1132C2×D3—21no—
1133C2×D3—21no—
1134C2×D3—21no—
1135C2×D3—21no—
1136C2×D3—32no—
1137C2×D3—32no—
1138C2×D3—32no—
1139C2×D3—32no—
1140C2×D3—32no—
1141C2×D3—32no—
1142C2×D3—62no—
1143C2×D3—62no—
1144C2×D3—62no—
1145C2×D3—61no—
1146C2×D3—61no—
1147C2×D3—61no—
1148C2×D3—61no—
1149C2×D3—61no—
1150C2×D3—61no—
1151C2×D3—61no—
1152C2×D3—61no—
1153C2×D3—61no—
1154C2×D3—61no—
1155C2×D3—61no—
1156C2×D3—61no—
1157C2×D3—62no—
1158C2×D3—61no—
1159C2×D3—61no—
1160C2×D3—61no—
1161C2×D3—61no—
1162C2×D3—61no—
1163C2×D3—61no—
1164C2×D3—121no—
1165C2×D3—121no—
1166C2×D3—121no—
1167C2×D3—121no—
1168C2×D3—121no—
1169C2×D3—121no—
1170C2×D3—121no—
1171C2×D3—121no—
1172C2×D3—124no—
1173C2×D3—124no—
1174C2×D3—124no—
1175C2×D3—124no—
1176C2×D3—128no—
1177C2×D3—364no—
1178C2×D3—364no—
1179C2×D3—364no—
1180C3×C4—62no—
1181C3×C4—61no—
1182C3×C4—61no—
1183C3×C4—61no—
1184C3×C4—61no—
1185C3×C4—61no—
1186C3×C4—61no—
1187C3×C4—61no—
1188C3×C4—61no—
1189C3×C4—121no—
1190C3×C4—121no—
1191C3×C4—121no—
1192C3×C4—181no—
1193C3×C4—181no—
1194Dic3—21no—
1195Dic3—21no—
1196Dic3—21no—
1197Dic3—21no—
1198Dic3—61no—
1199Dic3—61no—
1200Dic3—61no—
1201Dic3—61no—
1202Dic3—121no—
1203Dic3—121no—
1204Dic3—181no—
1205Dic3—181no—
1206Dic3—181no—
1207Dic3—181no—
1208Dic3—181no—
1209Dic3—181no—
1210Dic3—361no—
1211Dic3—361no—
1212Dic3—361no—
1213Dic3—361no—
1214Dic3—361no—
1215Dic3—361no—
1216Dic3—721no—
1217Dic3—721no—
1218C32—21no—
1219C32—21no—
1220C32—21no—
1221C32—41no—
1222C32#558911yescharacteristic, complemented
1223C32#558911yescharacteristic, complemented
1224C32#560511yescharacteristic, complemented
1225C23—31no—
1226C23—31no—
1227C23—91no—
1228C23—91no—
1229C23—91no—
1230C23—91no—
1231C23—182no—
1232C23—182no—
1233C23—274no—
1234C23—361no—
1235C23—361no—
1236C23—361no—
1237C23—361no—
1238C23—1081no—
1239C23—1081no—
1240C23D3311yescharacteristic
1241D4—121no—
1242D4—121no—
1243D4—182no—
1244D4—182no—
1245D4—182no—
1246D4—182no—
1247D4—361no—
1248D4—542no—
1249D4—542no—
1250D4—542no—
1251D4—542no—
1252D4—1081no—
1253C2×C4—31no—
1254C2×C4—31no—
1255C2×C4—31no—
1256C2×C4—31no—
1257C2×C4—91no—
1258C2×C4—91no—
1259C2×C4—271no—
1260C2×C4—271no—
1261C2×C4—361no—
1262C2×C4—542no—
1263C2×C4—542no—
1264C2×C4—1081no—
1265C2×C3—21no—
1266C2×C3—21no—
1267C2×C3—21no—
1268C2×C3—21no—
1269C2×C3—21no—
1270C2×C3—21no—
1271C2×C3—21no—
1272C2×C3—21no—
1273C2×C3—21no—
1274C2×C3—42no—
1275C2×C3—41no—
1276C2×C3—41no—
1277C2×C3—41no—
1278C2×C3—41no—
1279C2×C3—41no—
1280C2×C3—41no—
1281C2×C3—81no—
1282C2×C3—81no—
1283C2×C3—82no—
1284C2×C3—121no—
1285C2×C3—121no—
1286C2×C3—121no—
1287C2×C3—121no—
1288C2×C3—182no—
1289C2×C3—182no—
1290C2×C3—182no—
1291C2×C3—241no—
1292C2×C3—241no—
1293C2×C3—361no—
1294C2×C3#6430711yescharacteristic
1295C2×C3D32×D411yescharacteristic
1296C2×C3D32×D411yescharacteristic
1297C2×C3D32×D411yescharacteristic
1298C2×C3#6431311yescharacteristic
1299C2×C3#6431311yescharacteristic
1300C2×C3#6431411yescharacteristic
1301C2×C3#6433011yescharacteristic
1302C2×C3#6433011yescharacteristic
1303D3—41no—
1304D3—41no—
1305D3—62no—
1306D3—62no—
1307D3—62no—
1308D3—62no—
1309D3—62no—
1310D3—62no—
1311D3—122no—
1312D3—122no—
1313D3—122no—
1314D3—122no—
1315D3—121no—
1316D3—121no—
1317C22—21no—
1318C22—21no—
1319C22—21no—
1320C22—61no—
1321C22—61no—
1322C22—61no—
1323C22—61no—
1324C22—61no—
1325C22—61no—
1326C22—92no—
1327C22—92no—
1328C22—92no—
1329C22—181no—
1330C22—181no—
1331C22—181no—
1332C22—181no—
1333C22—181no—
1334C22—181no—
1335C22—181no—
1336C22—181no—
1337C22—181no—
1338C22—364no—
1339C22—364no—
1340C22—1084no—
1341C22C2×D3311yescharacteristic
1342C4—61no—
1343C4—61no—
1344C4—61no—
1345C4—61no—
1346C4—181no—
1347C4—181no—
1348C4—541no—
1349C4—541no—
1350C3—21no—
1351C3—21no—
1352C3—21no—
1353C3—41no—
1354C3#1059426311yescharacteristic, complemented
1355C3#1059528011yescharacteristic, complemented
1356C3#1059528111yescharacteristic, complemented
1357C2—41no—
1358C2—121no—
1359C2—121no—
1360C2—182no—
1361C2—182no—
1362C2—182no—
1363C2—361no—
1364C2#1172441511yescharacteristic
1365C2#1172441811yescharacteristic
1366C2#1172444011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×#88953C2semidirect
3. #11723634C2semidirect
4. #11723631C2semidirect
5. #11723621C2semidirect
6. C3×#63983C2semidirect
7. C3×#63981C2semidirect
8. C3×#63958C2semidirect
9. #11722998C2semidirect
10. #11722997C2semidirect
11. #11722994C2semidirect
12. #11722967C2semidirect
13. #11722957C2semidirect
14. #11722947C2semidirect
15. #11722905C2semidirect
19. C23×C3×C3⋊D3C22semidirect
21. C22×C3×D32C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×#67C22semidirect
28. C2×#6295C22semidirect
29. C2×#6294C22semidirect
31. C2×#6290C22semidirect
32. C2×#6290C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
34. C2×Dic3×C3⋊D3C22semidirect
36. C2×C3×#626C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#624C22semidirect
40. #88864C22semidirect
41. C32×#217C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
71. #63983D3semidirect
72. #63981D3semidirect
88. #63958D3semidirect
116. C2×#1113D4semidirect
147. C23×C3⋊D3C2×D3semidirect
156. C22×D32C2×D3semidirect
163. C2×#638C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
179. C2×C3×#67C2×D3semidirect
180. C2×C3×#67C2×D3semidirect
196. C2×#626C2×D3semidirect
197. C2×#626C2×D3semidirect
210. C2×#624C2×D3semidirect
239. C3×#217C2×D3semidirect
240. C3×#217C2×D3semidirect
261. Dic3⋊Dic3C2×D3semidirect
262. #3722C2×D3semidirect
263. #3722C2×D3semidirect
264. #3722C2×D3semidirect
277. (C2×D3)⋊Dic3C2×D3semidirect
278. (C2×D3)⋊Dic3C2×D3semidirect
279. (C2×D3)⋊Dic3C2×D3semidirect
577. C2×#67D32semidirect
578. C2×#67D32semidirect
627. #217D32semidirect
824. C33#534semidirect
1222. C32#5589semidirect
1223. C32#5589semidirect
1224. C32#5605semidirect
1354. C3#10594263semidirect
1355. C3#10595280semidirect
1356. C3#10595281semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#890492
C2×#889532
#117236342
#117236312
#117236212
C3×#639832
C3×#639812
C3×#639582
#117229982
#117229972
#117229942
#117229672
#117229572
#117229472
#117229052
#105952813
#105952803
#105942633