Finite Group Databasebeta

← #13172891

Subgroups — #13172891

Order 1728.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#88962C211yesmaximal, characteristic, complemented
3#11723723C211yesmaximal, characteristic, complemented
4#11723628C211yesmaximal, characteristic, complemented
5#11723599C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63970C211yesmaximal, characteristic, complemented
8C3×#63959C211yesmaximal, characteristic, complemented
9#11722998C211yesmaximal, characteristic, complemented
10#11722974C211yesmaximal, characteristic, complemented
11#11722965C211yesmaximal, characteristic, complemented
12#11722949C211yesmaximal, characteristic, complemented
13#11722937C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10595294—31nomaximal
17#10595243—31nomaximal
18#10594281—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic, complemented
24C2×#6294C2211yescharacteristic, complemented
25C2×#6294C2211yescharacteristic, complemented
26C3⋊D3×#67—24no—
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic, complemented
29C2×#6290C2211yescharacteristic
30C2×#6289C2211yescharacteristic, complemented
31C2×#6289C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic
33C2×C3×#627C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#625C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88962—24no—
39C3×#3757C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88814C2211yescharacteristic
43#88814C2211yescharacteristic
44#88807C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×#67—61no—
60C2×#3804—31no—
61C2×#3799—31no—
62C2×#3796—31no—
63#64147—31no—
64#64092—31no—
65C3×#939—31no—
66C3×#938—31no—
67C3×#937—31no—
68C3×#936—31no—
69C3×#885—31no—
70C3×#882—31no—
71#63983—31no—
72#63981—31no—
73#63981D311yescharacteristic, complemented
74#63975—31no—
75#63975—31no—
76#63975—31no—
77#63975—61no—
78#63974—31no—
79#63974—31no—
80Dic3×#67—31no—
81#63970—31no—
82#63970D311yescharacteristic, complemented
83D3×#217—31no—
84D3×#217—31no—
85#63959D311yescharacteristic, complemented
86#63958—31no—
87#63958—31no—
88#63958—31no—
89#63958—61no—
90#63922—31no—
91#63921—31no—
92#63921—31no—
93C4×#626—31no—
94#63894—31no—
95#63893—31no—
96Dic3×D12—31no—
97#63891—31no—
98#63891—31no—
99#63887—31no—
100#63885—31no—
101#63881—31no—
102#63880—31no—
103#63871—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—41no—
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C32×#67—22no—
123C32×#67—41no—
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6294—22no—
129#6294—41no—
130#6292D414yescomplemented
131#6291—22no—
132#6290—22no—
133#6289—22no—
134#6289—41no—
135Dic3×C3⋊D3—22no—
136C3×#627—22no—
137C3×#626—22no—
138C3×#626—22no—
139C3×#625—41no—
140C3×D3×Dic3—22no—
141#5676—91no—
142#5612—91no—
143#5591—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C23×C3×D3—61no—
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C2×C32×D4—31no—
153C2×C32×D4—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—61no—
162C2×#638—121no—
163D4×C3⋊D3—64no—
164C2×C4⋊(C3⋊D3)—31no—
165C2×C4×C3⋊D3—31no—
166C2×C4×C3⋊D3—31no—
167C2×C4×C3⋊D3—31no—
168C2×C3×#67—21no—
169C2×C3×#67—21no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67C2×D311yescharacteristic
175C2×C3×#67C2×D311yescharacteristic
176C2×C3×#67C2×D311yescharacteristic, complemented
177C2×C3×#67C2×D311yescharacteristic, complemented
178C22×C3×Dic3—31no—
179C2×C3×D12—31no—
180C2×C3×D12—31no—
181C2×C3×C4×D3—31no—
182C2×C3×Dic6—31no—
183C2×C3×Dic6—31no—
184D3×#67—64no—
185D3×#67—64no—
186D3×#67—68no—
187C2×#627C2×D311yescharacteristic, complemented
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—61no—
193C2×#626—61no—
194C2×#626C2×D311yescharacteristic
195C2×#626C2×D311yescharacteristic, complemented
196C2×#625—31no—
197C2×#625—31no—
198C2×#625—61no—
199C2×#625C2×D311yescharacteristic, complemented
200C2×#624—31no—
201C2×#624—31no—
202C2×#624—31no—
203C2×#624—31no—
204C2×#624—31no—
205C2×#624—31no—
206C2×#624—61no—
207C2×#624—61no—
208#3804—64no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—61no—
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217#3799—64no—
218#3796—64no—
219C32×C22⋊C4—31no—
220#3757—31no—
221#3757C2×D311yescharacteristic, complemented
222#3757C2×D311yescharacteristic, complemented
223#3752—31no—
224C4⋊(C3⋊Dic3)—31no—
225C4⋊(C3⋊Dic3)—31no—
226#3750—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—61no—
236C3×#217—61no—
237C3×#217C2×D311yescharacteristic, complemented
238C3×#217C2×D311yescharacteristic, complemented
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
247C3×Dic3⋊C4—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3—61no—
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—61no—
265#3722C2×D311yescharacteristic
266#3722C2×D311yescharacteristic, complemented
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)⋊Dic3C2×D311yescharacteristic, complemented
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33C2411yescharacteristic
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)C2×D412yes—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—44no—
290C2×C3×C3⋊D3C2×D412yes—
291C2×C3×C3⋊D3#4112yescomplemented
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298D3×C3⋊D3—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3C2×D412yes—
308C22×#67—91no—
309C2×#239—91no—
310C2×#237—91no—
311C2×D3×D4—91no—
312C2×D3×D4—91no—
313C2×D3×D4—181no—
314C2×#235—91no—
315C3×#124—91no—
316C3×#121—91no—
317C3×#120—91no—
318C2×#217—91no—
319#946—91no—
320#939—31no—
321#939—91no—
322#938—31no—
323#938—91no—
324#938—91no—
325#938—91no—
326#938—181no—
327#937—31no—
328#937—91no—
329#937—91no—
330#936—31no—
331D4×Dic3—91no—
332C4×#67—91no—
333#897—91no—
334#893—91no—
335#886—91no—
336#885—31no—
337#884—91no—
338#884—91no—
339#883—91no—
340#883—91no—
341#883—91no—
342#883—91no—
343#883—91no—
344#883—181no—
345#882—31no—
346#882—91no—
347#67⋊C4—91no—
348D3×C22⋊C4—91no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353#878—91no—
354C4×D12—91no—
355C4×D12—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C22×C3⋊D3—22no—
366C22×C3⋊D3—22no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—41no—
371C22×C3⋊D3—61no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—62no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3×D3—21no—
381C22×C3×D3—21no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—61no—
387C22×C3×D3—61no—
388C22×C3×D3—62no—
389C22×C3×D3—62no—
390C22×C3×D3—62no—
391C22×C3×D3—62no—
392C22×C3×D3—64no—
393C22×C3×D3—122no—
394C22×C3×D3—121no—
395C22×C3×D3—121no—
396C22×C3×D3—122no—
397C22×C3×D3C22×D311yescharacteristic
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—62no—
404C2×D32—62no—
405C2×D32—64no—
406C2×D32—122no—
407C2×D32—121no—
408C2×D32—121no—
409C2×D32—122no—
410C32×D4—62no—
411C32×D4—121no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—31no—
416#638—62no—
417#638—62no—
418#638—62no—
419#638—62no—
420#638—62no—
421#638—64no—
422#638—122no—
423#638—122no—
424#638—124no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—121no—
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C4⋊(C3⋊D3)—34no—
437C4×C3⋊D3—62no—
438C4×C3⋊D3—62no—
439C4×C3⋊D3—121no—
440C3×#67—24no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—41no—
444C3×#67—41no—
445C3×#67—42no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—121no—
449C3×#67—121no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—62no—
467C2×C3×Dic3C22×D311yescharacteristic
468C2×C3×Dic3C22×D311yescharacteristic
469C2×C3×Dic3C22×D311yescharacteristic
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C3×D12—62no—
476C3×D12—62no—
477C3×C4×D3—62no—
478C3×Dic6—62no—
479C3×Dic6—62no—
480#627—22no—
481#626—22no—
482#626—22no—
483#626—34no—
484#626—34no—
485#626—64no—
486#626—62no—
487#626—62no—
488#626—122no—
489#625—41no—
490#625—62no—
491#625—62no—
492#625—64no—
493#624—62no—
494#624—62no—
495#624—62no—
496#624—122no—
497#624—121no—
498#624—121no—
499#624—122no—
500#624—121no—
501D3×Dic3—22no—
502D3×Dic3—64no—
503D3×Dic3—62no—
504D3×Dic3—62no—
505D3×Dic3—62no—
506D3×Dic3—62no—
507D3×Dic3—121no—
508D3×Dic3—121no—
509#546—271noSylow
510C2×C33—41no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—22no—
515C3×C3⋊D3—22no—
516C3×C3⋊D3—22no—
517C32×D3—41no—
518C32×D3—41no—
519C24×C3—91no—
520C23×D3—31no—
521C23×D3—31no—
522C23×D3—61no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—91no—
526C23×D3—181no—
527C2×C3×Q8—91no—
528C2×C3×D4—31no—
529C2×C3×D4—31no—
530C2×C3×D4—31no—
531C2×C3×D4—31no—
532C2×C3×D4—61no—
533C2×C3×D4—61no—
534C2×C3×D4—91no—
535C2×C3×D4—91no—
536C2×C3×D4—91no—
537C22×C3×C4—91no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—91no—
543C2×#67—91no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—181no—
552C2×#67—181no—
553C2×#67—181no—
554C2×#67—181no—
555C2×#67—181no—
556C2×#67—184no—
557C2×#67—361no—
558C2×#67D3211yescharacteristic
559C2×#67D3211yescharacteristic, complemented
560C22×Dic3—31no—
561C22×Dic3—91no—
562C22×Dic3—91no—
563C22×Dic3—91no—
564#239—184no—
565#237—184no—
566D3×D4—184no—
567D3×D4—184no—
568D3×D4—188no—
569#235—184no—
570C2×D12—31no—
571C2×D12—31no—
572C2×D12—91no—
573C2×D12—91no—
574C2×D12—91no—
575C2×D12—181no—
576C2×C4×D3—31no—
577C2×C4×D3—91no—
578C2×C4×D3—91no—
579C2×C4×D3—91no—
580C2×C4×D3—91no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×C4×D3—91no—
589C2×C4×D3—181no—
590C2×C4×D3—181no—
591C2×C4×D3—181no—
592C2×Dic6—31no—
593C2×Dic6—31no—
594C3×C4⋊C4—91no—
595C3×C22⋊C4—31no—
596C3×C22⋊C4—31no—
597C3×C22⋊C4—61no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605C3×C42—91no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—31no—
612#217—31no—
613#217—61no—
614#217—61no—
615#217—91no—
616#217—91no—
617#217—91no—
618#217—91no—
619#217—181no—
620#217D3211yescharacteristic, complemented
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—31no—
624(C2×D3)⋊C4—31no—
625(C2×D3)⋊C4—31no—
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—181no—
637C4⋊Dic3—31no—
638C4⋊Dic3—91no—
639C4⋊Dic3—91no—
640C4⋊Dic3—91no—
641C4⋊Dic3—91no—
642C4⋊Dic3—91no—
643C4⋊Dic3—181no—
644C4⋊Dic3—181no—
645Dic3⋊C4—31no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650Dic3⋊C4—181no—
651C4×Dic3—31no—
652C4×Dic3—31no—
653C22×C32—21no—
654C22×C32—22no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—42no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—81no—
683C22×C32—81no—
684C22×C32C23×D311yescharacteristic
685C22×C32C23×D311yescharacteristic
686C22×C32C23×D311yescharacteristic
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—32no—
692C2×C3⋊D3—32no—
693C2×C3⋊D3—32no—
694C2×C3⋊D3—44no—
695C2×C3⋊D3—62no—
696C2×C3⋊D3—62no—
697C2×C3⋊D3—62no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—122no—
705C2×C3⋊D3—121no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—124no—
712C2×C3⋊D3—241no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3D3×D412yes—
715C2×C3⋊D3#23712yescomplemented
716C2×C3×D3—22no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—21no—
723C2×C3×D3—21no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—21no—
729C2×C3×D3—32no—
730C2×C3×D3—32no—
731C2×C3×D3—32no—
732C2×C3×D3—32no—
733C2×C3×D3—41no—
734C2×C3×D3—41no—
735C2×C3×D3—41no—
736C2×C3×D3—41no—
737C2×C3×D3—41no—
738C2×C3×D3—62no—
739C2×C3×D3—62no—
740C2×C3×D3—62no—
741C2×C3×D3—62no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—61no—
748C2×C3×D3—61no—
749C2×C3×D3—61no—
750C2×C3×D3—121no—
751C2×C3×D3—121no—
752C2×C3×D3—124no—
753C2×C3×D3—124no—
754C2×C3×D3—128no—
755D32—124no—
756D32—124no—
757D32—128no—
758C32×C4—32no—
759C32×C4—61no—
760C32×C4—61no—
761C32×C4—61no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—21no—
766C3⋊Dic3—61no—
767C3⋊Dic3—62no—
768C3⋊Dic3—61no—
769C3⋊Dic3—61no—
770C3⋊Dic3—121no—
771C3⋊Dic3—121no—
772C3⋊Dic3—122no—
773C3×Dic3—22no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—22no—
781C3×Dic3—41no—
782C3×Dic3—41no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—121no—
792C3×Dic3—121no—
793C3×Dic3—121no—
794C3×Dic3—121no—
795C3×Dic3D3×D412yes—
796C3×Dic3D3×D412yes—
797C2×#41—271no—
798C22×D4—271no—
799#124—91no—
800#123—271no—
801#123—271no—
802C22⋊Q8—271no—
803#121—91no—
804#121—271no—
805#121—271no—
806#120—91no—
807#120—271no—
808C4×D4—271no—
809C4×D4—271no—
810C2×C22⋊C4—271no—
811C2×C22⋊C4—271no—
812C33#54611yescharacteristic, complemented, Sylow
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—31no—
819C23×C3—31no—
820C23×C3—41no—
821C23×C3—61no—
822C23×C3—61no—
823C23×C3—91no—
824C23×C3—91no—
825C23×C3—182no—
826C23×C3—182no—
827C23×C3—361no—
828C23×C3C2×D3211yescharacteristic
829C23×C3C2×D3211yescharacteristic
830C23×C3C2×D3211yescharacteristic
831C22×D3—31no—
832C22×D3—31no—
833C22×D3—31no—
834C22×D3—31no—
835C22×D3—61no—
836C22×D3—61no—
837C22×D3—62no—
838C22×D3—62no—
839C22×D3—62no—
840C22×D3—62no—
841C22×D3—64no—
842C22×D3—91no—
843C22×D3—91no—
844C22×D3—91no—
845C22×D3—122no—
846C22×D3—121no—
847C22×D3—121no—
848C22×D3—122no—
849C22×D3—181no—
850C22×D3—181no—
851C22×D3—181no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—182no—
855C22×D3—182no—
856C22×D3—182no—
857C22×D3—182no—
858C22×D3—184no—
859C22×D3—361no—
860C22×D3—362no—
861C22×D3—361no—
862C22×D3—361no—
863C22×D3—361no—
864C22×D3—362no—
865C22×D3C2×D3211yescharacteristic
866C22×D3C2×D3211yescharacteristic
867C3×Q8—182no—
868C3×D4—62no—
869C3×D4—62no—
870C3×D4—64no—
871C3×D4—121no—
872C3×D4—121no—
873C3×D4—122no—
874C3×D4—182no—
875C3×D4—182no—
876C3×D4—361no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—31no—
881C2×C3×C4—31no—
882C2×C3×C4—31no—
883C2×C3×C4—31no—
884C2×C3×C4—31no—
885C2×C3×C4—61no—
886C2×C3×C4—61no—
887C2×C3×C4—61no—
888C2×C3×C4—61no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—91no—
892C2×C3×C4—91no—
893C2×C3×C4—182no—
894#67—22no—
895#67—41no—
896#67—62no—
897#67—62no—
898#67—94no—
899#67—121no—
900#67—121no—
901#67—182no—
902#67—182no—
903#67—182no—
904#67—182no—
905#67—182no—
906#67—184no—
907#67—182no—
908#67—182no—
909#67—182no—
910#67—184no—
911#67—362no—
912#67—362no—
913#67—362no—
914#67—364no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—61no—
924C2×Dic3—61no—
925C2×Dic3—61no—
926C2×Dic3—61no—
927C2×Dic3—62no—
928C2×Dic3—91no—
929C2×Dic3—91no—
930C2×Dic3—91no—
931C2×Dic3—181no—
932C2×Dic3—181no—
933C2×Dic3—181no—
934C2×Dic3—182no—
935C2×Dic3—182no—
936C2×Dic3—361no—
937C2×Dic3—361no—
938C2×Dic3C2×D3211yescharacteristic
939C2×Dic3C2×D3211yescharacteristic
940C2×Dic3C2×D3211yescharacteristic
941C2×Dic3C2×D3211yescharacteristic
942D12—62no—
943D12—62no—
944D12—94no—
945D12—94no—
946D12—184no—
947D12—182no—
948C4×D3—62no—
949C4×D3—182no—
950C4×D3—182no—
951C4×D3—182no—
952C4×D3—182no—
953C4×D3—182no—
954C4×D3—182no—
955C4×D3—182no—
956C4×D3—184no—
957C4×D3—362no—
958C4×D3—361no—
959C4×D3—361no—
960C4×D3—361no—
961C4×D3—361no—
962C4×D3—361no—
963C4×D3—362no—
964Dic6—62no—
965Dic6—62no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—21no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—41no—
979C2×C32—42no—
980C2×C32—41no—
981C2×C32—41no—
982C2×C32—81no—
983C2×C32—81no—
984C2×C32—82no—
985C2×C32—121no—
986C2×C32—121no—
987C2×C32C2×D3×D411yescharacteristic
988C2×C32C2×D3×D411yescharacteristic
989C2×C32C2×D3×D411yescharacteristic
990C2×C32C2×#23711yescharacteristic
991C2×C32#100411yescharacteristic
992C2×C32#100411yescharacteristic
993C2×C32D3×#4111yescharacteristic
994C2×C32D3×#4111yescharacteristic
995C2×C32#100911yescharacteristic
996C3⋊D3—22no—
997C3⋊D3—22no—
998C3⋊D3—62no—
999C3⋊D3—62no—
1000C3⋊D3—62no—
1001C3⋊D3—122no—
1002C3⋊D3—122no—
1003C3⋊D3—122no—
1004C3⋊D3—242no—
1005C3×D3—42no—
1006C3×D3—41no—
1007C3×D3—41no—
1008C3×D3—41no—
1009C3×D3—41no—
1010C3×D3—64no—
1011C3×D3—62no—
1012C3×D3—62no—
1013C3×D3—62no—
1014C3×D3—62no—
1015C3×D3—81no—
1016C3×D3—122no—
1017C24—91no—
1018C24—271no—
1019#41—544no—
1020C2×Q8—91no—
1021C2×D4—31no—
1022C2×D4—31no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—271no—
1030C2×D4—544no—
1031C22×C4—91no—
1032C22×C4—271no—
1033C22×C4—271no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C22×C4—271no—
1037C4⋊C4—91no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C4⋊C4—271no—
1041C22⋊C4—31no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—91no—
1048C22⋊C4—91no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C22⋊C4—271no—
1053C42—91no—
1054C22×C3—22no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—21no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—42no—
1076C22×C3—41no—
1077C22×C3—62no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
1090C22×C3—81no—
1091C22×C3—81no—
1092C22×C3—92no—
1093C22×C3—92no—
1094C22×C3—121no—
1095C22×C3—121no—
1096C22×C3—121no—
1097C22×C3—121no—
1098C22×C3—121no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—181no—
1102C22×C3—181no—
1103C22×C3—364no—
1104C22×C3C22×D3211yescharacteristic
1105C22×C3C22×D3211yescharacteristic
1106C22×C3C22×D3211yescharacteristic
1107C2×D3—21no—
1108C2×D3—21no—
1109C2×D3—21no—
1110C2×D3—21no—
1111C2×D3—21no—
1112C2×D3—21no—
1113C2×D3—32no—
1114C2×D3—32no—
1115C2×D3—32no—
1116C2×D3—32no—
1117C2×D3—62no—
1118C2×D3—62no—
1119C2×D3—62no—
1120C2×D3—62no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—92no—
1130C2×D3—92no—
1131C2×D3—92no—
1132C2×D3—121no—
1133C2×D3—121no—
1134C2×D3—124no—
1135C2×D3—124no—
1136C2×D3—128no—
1137C2×D3—182no—
1138C2×D3—182no—
1139C2×D3—182no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—181no—
1143C2×D3—181no—
1144C2×D3—181no—
1145C2×D3—181no—
1146C2×D3—362no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—361no—
1151C2×D3—361no—
1152C2×D3—361no—
1153C2×D3—364no—
1154C2×D3—364no—
1155C2×D3—364no—
1156C2×D3—368no—
1157C2×D3—721no—
1158C2×D3—721no—
1159C3×C4—32no—
1160C3×C4—32no—
1161C3×C4—62no—
1162C3×C4—62no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—61no—
1167C3×C4—61no—
1168C3×C4—61no—
1169C3×C4—121no—
1170C3×C4—121no—
1171C3×C4—181no—
1172C3×C4—181no—
1173C3×C4—181no—
1174C3×C4—181no—
1175Dic3—21no—
1176Dic3—21no—
1177Dic3—21no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—121no—
1187Dic3—121no—
1188Dic3—121no—
1189Dic3—121no—
1190Dic3—182no—
1191Dic3—181no—
1192Dic3—181no—
1193Dic3—181no—
1194Dic3—361no—
1195Dic3—361no—
1196Dic3—362no—
1197Dic3#381112yes—
1198C32—21no—
1199C32—21no—
1200C32—21no—
1201C32—41no—
1202C32#559111yescharacteristic, complemented
1203C32#561211yescharacteristic, complemented
1204C32#567611yescharacteristic, complemented
1205C23—31no—
1206C23—31no—
1207C23—91no—
1208C23—91no—
1209C23—182no—
1210C23—182no—
1211C23—271no—
1212C23—361no—
1213C23—542no—
1214C23—542no—
1215C23—1081no—
1216C23D3311yescharacteristic
1217Q8—182no—
1218D4—62no—
1219D4—121no—
1220D4—182no—
1221D4—182no—
1222D4—274no—
1223D4—361no—
1224D4—542no—
1225D4—542no—
1226D4—542no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—31no—
1230C2×C4—31no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—91no—
1235C2×C4—182no—
1236C2×C4—271no—
1237C2×C4—542no—
1238C2×C4—542no—
1239C2×C4—542no—
1240C2×C4—1081no—
1241C2×C4—1081no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—42no—
1252C2×C3—41no—
1253C2×C3—41no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—41no—
1257C2×C3—41no—
1258C2×C3—81no—
1259C2×C3—81no—
1260C2×C3—82no—
1261C2×C3—122no—
1262C2×C3—121no—
1263C2×C3—121no—
1264C2×C3—121no—
1265C2×C3—121no—
1266C2×C3—182no—
1267C2×C3—182no—
1268C2×C3—241no—
1269C2×C3#6430711yescharacteristic
1270C2×C3D32×D411yescharacteristic
1271C2×C3D32×D411yescharacteristic
1272C2×C3D3×#23711yescharacteristic
1273C2×C3D3×#23711yescharacteristic
1274C2×C3#6431211yescharacteristic
1275C2×C3#6431411yescharacteristic
1276C2×C3C2×#381111yescharacteristic
1277C2×C3#6433011yescharacteristic
1278D3—41no—
1279D3—41no—
1280D3—64no—
1281D3—62no—
1282D3—62no—
1283D3—62no—
1284D3—62no—
1285D3—122no—
1286D3—182no—
1287D3—182no—
1288D3—182no—
1289D3—362no—
1290D3—362no—
1291D3—362no—
1292D3—722no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—61no—
1297C22—61no—
1298C22—61no—
1299C22—61no—
1300C22—61no—
1301C22—61no—
1302C22—92no—
1303C22—92no—
1304C22—181no—
1305C22—181no—
1306C22—181no—
1307C22—181no—
1308C22—272no—
1309C22—364no—
1310C22—541no—
1311C22—541no—
1312C22—1084no—
1313C22C2×D3311yescharacteristic
1314C4—32no—
1315C4—61no—
1316C4—61no—
1317C4—61no—
1318C4—181no—
1319C4—181no—
1320C4—181no—
1321C4—181no—
1322C4—541no—
1323C3—21no—
1324C3—21no—
1325C3—21no—
1326C3—41no—
1327C3#1059428111yescharacteristic, complemented
1328C3#1059524311yescharacteristic, complemented
1329C3#1059529411yescharacteristic, complemented
1330C2—41no—
1331C2—121no—
1332C2—121no—
1333C2—182no—
1334C2—182no—
1335C2—542no—
1336C2#1172440811yescharacteristic
1337C2#1172441811yescharacteristic
1338C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#88962C2semidirect
3. #11723723C2semidirect
4. #11723628C2semidirect
5. #11723599C2semidirect
6. C3×#63981C2semidirect
7. C3×#63970C2semidirect
8. C3×#63959C2semidirect
9. #11722998C2semidirect
10. #11722974C2semidirect
11. #11722965C2semidirect
12. #11722949C2semidirect
13. #11722937C2semidirect
14. Dic3×#626C2semidirect
15. #11722906C2semidirect
23. C2×C32×#67C22semidirect
24. C2×#6294C22semidirect
25. C2×#6294C22semidirect
28. C2×#6291C22semidirect
30. C2×#6289C22semidirect
31. C2×#6289C22semidirect
33. C2×C3×#627C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#625C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. C3×#3757C22semidirect
41. C32×#217C22semidirect
44. #88807C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88804C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
73. #63981D3semidirect
82. #63970D3semidirect
85. #63959D3semidirect
130. #6292D4semidirect
176. C2×C3×#67C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
187. C2×#627C2×D3semidirect
195. C2×#626C2×D3semidirect
199. C2×#625C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
221. #3757C2×D3semidirect
222. #3757C2×D3semidirect
237. C3×#217C2×D3semidirect
238. C3×#217C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
266. #3722C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
291. C2×C3×C3⋊D3#41semidirect
559. C2×#67D32semidirect
620. #217D32semidirect
715. C2×C3⋊D3#237semidirect
812. C33#546semidirect
1202. C32#5591semidirect
1203. C32#5612semidirect
1204. C32#5676semidirect
1327. C3#10594281semidirect
1328. C3#10595243semidirect
1329. C3#10595294semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#889622
#117237232
#117236282
#117235992
C3×#639812
C3×#639702
C3×#639592
#117229982
#117229742
#117229652
#117229492
#117229372
Dic3×#6262
#117229062
#105952943
#105952433
#105942813