Finite Group Databasebeta

← #13172922

Subgroups — #13172922

Order 1728.

1670 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#88961C211yesmaximal, characteristic, complemented
3#11723634C211yesmaximal, characteristic, complemented
4#11723615C211yesmaximal, characteristic, complemented
5#11723591C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63979C211yesmaximal, characteristic, complemented
8C3×#63971C211yesmaximal, characteristic, complemented
9#11723029C211yesmaximal, characteristic, complemented
10#11723010C211yesmaximal, characteristic, complemented
11#11722960C211yesmaximal, characteristic, complemented
12#11722955C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722951C211yesmaximal, characteristic, complemented
15#11722922C211yesmaximal, characteristic, complemented
16#10595299—31nomaximal
17#10595286—31nomaximal
18#10594269—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic, complemented
25#89049—24no—
26C2×#6295C2211yescharacteristic
27C2×#6295C2211yescharacteristic
28C2×#6294C2211yescharacteristic
29C2×#6293C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic, complemented
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#626C2211yescharacteristic, complemented
37C2×C3×#626C2211yescharacteristic, complemented
38C2×C3×#626C2211yescharacteristic, complemented
39C2×C3×#625C2211yescharacteristic, complemented
40C2×C3×D3×Dic3C2211yescharacteristic, complemented
41#88961—24no—
42#88864C2211yescharacteristic, complemented
43C32×#217C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, complemented
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51C3×#3724C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic, complemented
54C3×#3722C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3805—31no—
60C2×#3804—31no—
61C2×#3795—31no—
62#64148—31no—
63#64146—31no—
64#64094—31no—
65C3×#940—31no—
66C3×#940—31no—
67C3×#939—31no—
68C3×#937—31no—
69C3×#884—31no—
70C3×#882—31no—
71#63983—31no—
72#63983—31no—
73#63981D311yescharacteristic, complemented
74#63980—31no—
75#63979—31no—
76#63979—31no—
77#63979D311yescharacteristic, complemented
78#63978—31no—
79#63976—31no—
80#63976—31no—
81#63976—61no—
82#63971D311yescharacteristic, complemented
83#63970—31no—
84#63970—31no—
85#63970—61no—
86#63959—31no—
87#63959—31no—
88#63959—61no—
89#63922—31no—
90#63922—31no—
91#63922—31no—
92#63922—31no—
93#63914—31no—
94#63913—31no—
95#63906—31no—
96#63886—31no—
97#63886—31no—
98#63885—31no—
99#63878—31no—
100#63877—31no—
101#63852—31no—
102#63852—31no—
103#63836—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—22no—
115C2×#1113—41no—
116C2×#1113—41no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638—22no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C32×#67—41no—
124C32×#67—41no—
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129#6295—22no—
130#6295—22no—
131#6294D414yescomplemented
132#6293—22no—
133#6290—22no—
134#6290—41no—
135#6290—41no—
136D3×C3⋊Dic3—22no—
137C3×#626—22no—
138C3×#626—41no—
139C3×#626—41no—
140C3×#626—41no—
141C3×#626—41no—
142C3×#625—22no—
143C3×D3×Dic3—22no—
144#5715—91no—
145#5607—91no—
146#5592—91no—
147C23×C3⋊D3C2×D311yescharacteristic
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3—61no—
151C22×D32—31no—
152C22×D32—31no—
153C22×D32—31no—
154C2×C32×D4—31no—
155C2×C32×D4—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638C2×D311yescharacteristic
160C2×#638C2×D311yescharacteristic
161C22×C3⋊Dic3—31no—
162C2×#634—31no—
163C2×C3×#67—21no—
164C2×C3×#67—21no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
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—31no—
176C2×C3×#67—61no—
177C2×C3×#67—61no—
178C2×C3×#67C2×D311yescharacteristic, complemented
179C2×C3×#67C2×D311yescharacteristic, complemented
180C2×C3×#67C2×D311yescharacteristic, complemented
181C2×C3×#67C2×D311yescharacteristic, complemented
182C22×C3×Dic3—31no—
183C2×C3×D12—31no—
184C2×C3×D12—31no—
185C2×C3×D12—31no—
186C2×C3×D12—31no—
187C2×C3×D12—31no—
188C2×C3×C4×D3—31no—
189#3811—64no—
190D3×#67—64no—
191D3×#67—64no—
192C2×#627—31no—
193C2×#627—31no—
194C2×#627—61no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626C2×D311yescharacteristic
200C2×#626C2×D311yescharacteristic, complemented
201C2×#626C2×D311yescharacteristic, complemented
202C2×#626C2×D311yescharacteristic, complemented
203C2×#626C2×D311yescharacteristic, complemented
204C2×#625—31no—
205C2×#625—31no—
206C2×#625—31no—
207C2×#625—31no—
208C2×#625—31no—
209C2×#625—31no—
210C2×#625—31no—
211C2×#625—31no—
212C2×#625—61no—
213C2×#625—61no—
214C2×#625—61no—
215C2×#625C2×D311yescharacteristic, complemented
216C2×#624—31no—
217#3805—64no—
218#3804—64no—
219C2×D3×Dic3—31no—
220C2×D3×Dic3—31no—
221C2×D3×Dic3—31no—
222C2×D3×Dic3—31no—
223C2×D3×Dic3—61no—
224C2×D3×Dic3C2×D311yescharacteristic, complemented
225#3795—64no—
226C32×C22⋊C4—31no—
227#3757—31no—
228#3757—31no—
229#3757—31no—
230#3757—61no—
231#3757—61no—
232#3757—61no—
233#3757—121no—
234#3752—31no—
235#3752—31no—
236#3752—31no—
237#3752—31no—
238#3752—31no—
239#3750—31no—
240C4×C3⋊Dic3—31no—
241C3×#217—21no—
242C3×#217C2×D311yescharacteristic, complemented
243C3×#217C2×D311yescharacteristic, complemented
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×Dic3⋊C4—31no—
251C3×Dic3⋊C4—31no—
252C3×C4×Dic3—31no—
253C3×C4×Dic3—31no—
254#3724C2×D311yescharacteristic, complemented
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—61no—
258#3722C2×D311yescharacteristic
259#3722C2×D311yescharacteristic, complemented
260#3722C2×D311yescharacteristic, complemented
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
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—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3—61no—
276Dic32—31no—
277Dic32—31no—
278Dic32—61no—
279Dic32C2×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—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3—44no—
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⋊(C3⋊Dic3)—21no—
305C3⋊(C3⋊Dic3)—21no—
306C3×C3⋊Dic3C2×D412yes—
307C3×C3⋊Dic3C2×D412yes—
308C32×Dic3—21no—
309C32×Dic3—21no—
310C32×Dic3—21no—
311C32×Dic3—21no—
312C22×#67—91no—
313C2×#237—91no—
314C2×#237—91no—
315C2×D3×D4—91no—
316C2×D3×D4—91no—
317C2×#235—91no—
318C3×#127—91no—
319C3×#121—91no—
320C3×#120—91no—
321#953—91no—
322#940—31no—
323#940—31no—
324#940—91no—
325#940—91no—
326#940—91no—
327#939—31no—
328#939—91no—
329#939—91no—
330#939—91no—
331#939—91no—
332#939—91no—
333#939—181no—
334#938—91no—
335#937—31no—
336#937—91no—
337#937—91no—
338#937—91no—
339#937—91no—
340#937—91no—
341#937—91no—
342#937—181no—
343#936—91no—
344#930—91no—
345#895—91no—
346#892—91no—
347#885—91no—
348#885—91no—
349#885—91no—
350#885—91no—
351#885—181no—
352#884—31no—
353#884—91no—
354#882—31no—
355#882—91no—
356#882—91no—
357#877—91no—
358#875—91no—
359#872—91no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—31no—
364C23×C32—31no—
365C23×C32—41no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—22no—
370C22×C3⋊D3—41no—
371C22×C3⋊D3—41no—
372C22×C3⋊D3C22×D311yescharacteristic
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3×D3—21no—
377C22×C3×D3—21no—
378C22×C3×D3—31no—
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—61no—
387C22×C3×D3—61no—
388C22×C3×D3—61no—
389C22×C3×D3—61no—
390C22×C3×D3—62no—
391C22×C3×D3—62no—
392C22×C3×D3—122no—
393C22×C3×D3—121no—
394C22×C3×D3—121no—
395C22×C3×D3—121no—
396C22×C3×D3—121no—
397C22×C3×D3—122no—
398C22×C3×D3—122no—
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C22×C3×D3C22×D311yescharacteristic
402C22×C3×D3C22×D311yescharacteristic
403C2×D32—62no—
404C2×D32—62no—
405C2×D32—62no—
406C2×D32—121no—
407C2×D32—121no—
408C2×D32—121no—
409C2×D32—121no—
410C2×D32—121no—
411C2×D32—121no—
412C32×D4—121no—
413C32×D4—121no—
414C2×C32×C4—31no—
415C2×C32×C4—31no—
416C2×C32×C4—31no—
417C2×C32×C4—31no—
418#638—22no—
419#638—22no—
420#638—62no—
421#638—121no—
422#638—121no—
423C2×C3⋊Dic3—31no—
424C2×C3⋊Dic3—31no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—31no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—61no—
432C2×C3⋊Dic3—61no—
433C2×C3⋊Dic3—61no—
434C2×C3⋊Dic3—61no—
435C2×C3⋊Dic3—62no—
436C2×C3⋊Dic3—121no—
437C2×C3⋊Dic3—121no—
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440#634—62no—
441C3×#67—41no—
442C3×#67—41no—
443C3×#67—41no—
444C3×#67—41no—
445C3×#67—42no—
446C3×#67—42no—
447C3×#67—62no—
448C3×#67—62no—
449C3×#67—62no—
450C3×#67—62no—
451C3×#67—62no—
452C3×#67—62no—
453C3×#67—62no—
454C3×#67—122no—
455C3×#67—122no—
456C3×#67—121no—
457C3×#67—121no—
458C3×#67—121no—
459C3×#67—121no—
460C2×C3×Dic3—21no—
461C2×C3×Dic3—21no—
462C2×C3×Dic3—21no—
463C2×C3×Dic3—21no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—62no—
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C3×D12—62no—
480C3×D12—121no—
481C3×D12—121no—
482C3×D12—121no—
483C3×D12—121no—
484C3×C4×D3—62no—
485#627—62no—
486#627—62no—
487#627—122no—
488#626—22no—
489#626—41no—
490#626—41no—
491#626—41no—
492#626—41no—
493#626—62no—
494#626—62no—
495#626—62no—
496#626—62no—
497#625—22no—
498#625—62no—
499#625—62no—
500#625—62no—
501#625—62no—
502#625—122no—
503#625—121no—
504#625—121no—
505#625—121no—
506#625—121no—
507#625—122no—
508#625—122no—
509#624—34no—
510D3×Dic3—22no—
511D3×Dic3—34no—
512D3×Dic3—34no—
513D3×Dic3—62no—
514D3×Dic3—62no—
515D3×Dic3—122no—
516#535—271noSylow
517C2×C33—41no—
518C2×C33C22×D411yescharacteristic
519C2×C33H(5,𝔽2)11yescharacteristic
520C2×C33H(5,𝔽2)11yescharacteristic
521C3×C3⋊D3—22no—
522C3×C3⋊D3—41no—
523C3×C3⋊D3—41no—
524C3×C3⋊D3—41no—
525C32×D3—41no—
526C32×D3—41no—
527C24×C3—91no—
528C23×D3—31no—
529C23×D3—31no—
530C23×D3—61no—
531C23×D3—91no—
532C23×D3—91no—
533C23×D3—91no—
534C2×C3×D4—31no—
535C2×C3×D4—31no—
536C2×C3×D4—31no—
537C2×C3×D4—31no—
538C2×C3×D4—61no—
539C2×C3×D4—61no—
540C2×C3×D4—91no—
541C2×C3×D4—91no—
542C2×C3×D4—91no—
543C2×C3×D4—91no—
544C2×C3×D4—91no—
545C2×C3×D4—91no—
546C2×C3×D4—91no—
547C2×C3×D4—91no—
548C22×C3×C4—91no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—31no—
552C2×#67—31no—
553C2×#67—31no—
554C2×#67—31no—
555C2×#67—31no—
556C2×#67—31no—
557C2×#67—31no—
558C2×#67—31no—
559C2×#67—31no—
560C2×#67—61no—
561C2×#67—61no—
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—91no—
573C2×#67—91no—
574C2×#67—91no—
575C2×#67—181no—
576C2×#67—181no—
577C2×#67—181no—
578C2×#67—184no—
579C2×#67D3211yescharacteristic, complemented
580C2×#67D3211yescharacteristic, complemented
581C22×Dic3—31no—
582C22×Dic3—91no—
583C22×Dic3—91no—
584C22×Dic3—91no—
585C22×Dic3—181no—
586#237—184no—
587#237—184no—
588D3×D4—184no—
589D3×D4—184no—
590#235—184no—
591C2×D12—31no—
592C2×D12—31no—
593C2×D12—31no—
594C2×D12—31no—
595C2×D12—31no—
596C2×D12—91no—
597C2×D12—91no—
598C2×C4×D3—31no—
599C2×C4×D3—91no—
600C2×C4×D3—91no—
601C2×C4×D3—91no—
602C2×Dic6—91no—
603C2×Dic6—91no—
604C2×Dic6—91no—
605C2×Dic6—181no—
606C3×C4⋊C4—91no—
607C3×C22⋊C4—31no—
608C3×C22⋊C4—31no—
609C3×C22⋊C4—61no—
610C3×C22⋊C4—91no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C42—91no—
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—361no—
626#217D3211yescharacteristic, complemented
627(C2×D3)⋊C4—31no—
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—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
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—181no—
644(C2×D3)⋊C4—181no—
645(C2×D3)⋊C4—181no—
646(C2×D3)⋊C4—181no—
647(C2×D3)⋊C4—181no—
648C4⋊Dic3—91no—
649Dic3⋊C4—31no—
650Dic3⋊C4—31no—
651Dic3⋊C4—91no—
652Dic3⋊C4—91no—
653Dic3⋊C4—181no—
654C4×Dic3—31no—
655C4×Dic3—31no—
656C4×Dic3—91no—
657C4×Dic3—91no—
658C4×Dic3—91no—
659C4×Dic3—181no—
660C22×C32—21no—
661C22×C32—22no—
662C22×C32—21no—
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—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—42no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—61no—
686C22×C32—61no—
687C22×C32—61no—
688C22×C32—61no—
689C22×C32—81no—
690C22×C32—81no—
691C22×C32C23×D311yescharacteristic
692C22×C32C23×D311yescharacteristic
693C22×C32C23×D311yescharacteristic
694C2×C3⋊D3—21no—
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—21no—
705C2×C3⋊D3—44no—
706C2×C3⋊D3D3×D412yes—
707C2×C3×D3—22no—
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—41no—
723C2×C3×D3—41no—
724C2×C3×D3—41no—
725C2×C3×D3—41no—
726C2×C3×D3—41no—
727C2×C3×D3—62no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—62no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
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—61no—
748C2×C3×D3—61no—
749C2×C3×D3—61no—
750C2×C3×D3—61no—
751C2×C3×D3—121no—
752C2×C3×D3—121no—
753C2×C3×D3—121no—
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—124no—
762C2×C3×D3—124no—
763C2×C3×D3—128no—
764D32—124no—
765D32—124no—
766D32—124no—
767C32×C4—61no—
768C32×C4—61no—
769C32×C4—61no—
770C32×C4—61no—
771C3⋊Dic3—61no—
772C3⋊Dic3—61no—
773C3⋊Dic3—61no—
774C3⋊Dic3—61no—
775C3⋊Dic3—61no—
776C3⋊Dic3—61no—
777C3⋊Dic3—121no—
778C3⋊Dic3—121no—
779C3⋊Dic3—121no—
780C3⋊Dic3—121no—
781C3⋊Dic3—121no—
782C3⋊Dic3—121no—
783C3⋊Dic3—241no—
784C3⋊Dic3—241no—
785C3⋊Dic3D3×D412yes—
786C3⋊Dic3D3×D412yes—
787C3×Dic3—21no—
788C3×Dic3—21no—
789C3×Dic3—21no—
790C3×Dic3—21no—
791C3×Dic3—21no—
792C3×Dic3—21no—
793C3×Dic3—21no—
794C3×Dic3—21no—
795C3×Dic3—32no—
796C3×Dic3—32no—
797C3×Dic3—32no—
798C3×Dic3—32no—
799C3×Dic3—41no—
800C3×Dic3—41no—
801C3×Dic3—41no—
802C3×Dic3—41no—
803C3×Dic3—62no—
804C3×Dic3—62no—
805C2×#41—271no—
806C22×D4—271no—
807#127—91no—
808#127—271no—
809#124—271no—
810#124—271no—
811#121—91no—
812#121—271no—
813#121—271no—
814#121—271no—
815#120—91no—
816#120—271no—
817#120—271no—
818#120—271no—
819#117—271no—
820C33#53511yescharacteristic, complemented, Sylow
821C23×C3—21no—
822C23×C3—21no—
823C23×C3—21no—
824C23×C3—31no—
825C23×C3—31no—
826C23×C3—31no—
827C23×C3—31no—
828C23×C3—41no—
829C23×C3—61no—
830C23×C3—61no—
831C23×C3—91no—
832C23×C3—91no—
833C23×C3—91no—
834C23×C3—91no—
835C23×C3—182no—
836C23×C3—361no—
837C23×C3—361no—
838C23×C3C2×D3211yescharacteristic
839C23×C3C2×D3211yescharacteristic
840C23×C3C2×D3211yescharacteristic
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—31no—
846C22×D3—31no—
847C22×D3—31no—
848C22×D3—31no—
849C22×D3—61no—
850C22×D3—61no—
851C22×D3—61no—
852C22×D3—61no—
853C22×D3—62no—
854C22×D3—62no—
855C22×D3—122no—
856C22×D3—121no—
857C22×D3—121no—
858C22×D3—121no—
859C22×D3—121no—
860C22×D3—122no—
861C22×D3—122no—
862C22×D3—182no—
863C22×D3—182no—
864C22×D3—182no—
865C22×D3—361no—
866C22×D3—361no—
867C22×D3—361no—
868C22×D3—361no—
869C22×D3—361no—
870C22×D3—361no—
871C22×D3C2×D3211yescharacteristic
872C22×D3C2×D3211yescharacteristic
873C3×D4—121no—
874C3×D4—121no—
875C3×D4—121no—
876C3×D4—121no—
877C3×D4—122no—
878C3×D4—122no—
879C3×D4—182no—
880C3×D4—182no—
881C3×D4—182no—
882C3×D4—182no—
883C3×D4—361no—
884C3×D4—361no—
885C3×D4—361no—
886C3×D4—361no—
887C2×C3×C4—31no—
888C2×C3×C4—31no—
889C2×C3×C4—31no—
890C2×C3×C4—31no—
891C2×C3×C4—31no—
892C2×C3×C4—31no—
893C2×C3×C4—31no—
894C2×C3×C4—31no—
895C2×C3×C4—61no—
896C2×C3×C4—61no—
897C2×C3×C4—61no—
898C2×C3×C4—61no—
899C2×C3×C4—91no—
900C2×C3×C4—91no—
901C2×C3×C4—182no—
902#67—41no—
903#67—41no—
904#67—62no—
905#67—62no—
906#67—62no—
907#67—62no—
908#67—62no—
909#67—62no—
910#67—62no—
911#67—122no—
912#67—122no—
913#67—121no—
914#67—121no—
915#67—121no—
916#67—121no—
917#67—182no—
918#67—182no—
919#67—182no—
920#67—182no—
921#67—182no—
922#67—182no—
923#67—182no—
924#67—362no—
925#67—361no—
926#67—361no—
927#67—361no—
928#67—361no—
929#67—361no—
930#67—361no—
931#67—362no—
932#67—362no—
933C2×Dic3—31no—
934C2×Dic3—31no—
935C2×Dic3—31no—
936C2×Dic3—31no—
937C2×Dic3—61no—
938C2×Dic3—61no—
939C2×Dic3—62no—
940C2×Dic3—94no—
941C2×Dic3—91no—
942C2×Dic3—91no—
943C2×Dic3—91no—
944C2×Dic3—91no—
945C2×Dic3—91no—
946C2×Dic3—91no—
947C2×Dic3—181no—
948C2×Dic3—181no—
949C2×Dic3—181no—
950C2×Dic3—181no—
951C2×Dic3—181no—
952C2×Dic3—181no—
953C2×Dic3—182no—
954C2×Dic3—182no—
955C2×Dic3—361no—
956C2×Dic3—361no—
957C2×Dic3—362no—
958C2×Dic3C2×D3211yescharacteristic
959C2×Dic3C2×D3211yescharacteristic
960C2×Dic3C2×D3211yescharacteristic
961C2×Dic3C2×D3211yescharacteristic
962D12—62no—
963D12—121no—
964D12—121no—
965D12—121no—
966D12—121no—
967D12—182no—
968D12—182no—
969C4×D3—62no—
970C4×D3—94no—
971C4×D3—94no—
972C4×D3—182no—
973Dic6—182no—
974Dic6—182no—
975Dic6—182no—
976Dic6—362no—
977C2×C32—21no—
978C2×C32—21no—
979C2×C32—21no—
980C2×C32—21no—
981C2×C32—21no—
982C2×C32—21no—
983C2×C32—21no—
984C2×C32—21no—
985C2×C32—21no—
986C2×C32—41no—
987C2×C32—41no—
988C2×C32—41no—
989C2×C32—41no—
990C2×C32—42no—
991C2×C32—41no—
992C2×C32—41no—
993C2×C32—81no—
994C2×C32—81no—
995C2×C32—82no—
996C2×C32—121no—
997C2×C32—121no—
998C2×C32C2×D3×D411yescharacteristic
999C2×C32C2×D3×D411yescharacteristic
1000C2×C32C2×D3×D411yescharacteristic
1001C2×C32#100411yescharacteristic
1002C2×C32#100411yescharacteristic
1003C2×C32#100411yescharacteristic
1004C2×C32#100411yescharacteristic
1005C2×C32#100411yescharacteristic
1006C2×C32#100911yescharacteristic
1007C3⋊D3—22no—
1008C3⋊D3—41no—
1009C3⋊D3—41no—
1010C3⋊D3—41no—
1011C3×D3—42no—
1012C3×D3—41no—
1013C3×D3—41no—
1014C3×D3—41no—
1015C3×D3—41no—
1016C3×D3—62no—
1017C3×D3—62no—
1018C3×D3—81no—
1019C3×D3—122no—
1020C3×D3—122no—
1021C3×D3—121no—
1022C3×D3—121no—
1023C3×D3—121no—
1024C3×D3—121no—
1025C3×D3—121no—
1026C3×D3—121no—
1027C3×D3—241no—
1028C3×D3—241no—
1029C24—91no—
1030C24—271no—
1031#41—544no—
1032C2×Q8—271no—
1033C2×D4—31no—
1034C2×D4—31no—
1035C2×D4—91no—
1036C2×D4—91no—
1037C2×D4—91no—
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—
1049C22×C4—91no—
1050C22×C4—271no—
1051C22×C4—271no—
1052C4⋊C4—91no—
1053C4⋊C4—271no—
1054C22⋊C4—31no—
1055C22⋊C4—91no—
1056C22⋊C4—91no—
1057C22⋊C4—91no—
1058C22⋊C4—271no—
1059C22⋊C4—271no—
1060C22⋊C4—271no—
1061C22⋊C4—271no—
1062C22⋊C4—271no—
1063C22⋊C4—271no—
1064C42—91no—
1065C42—271no—
1066C22×C3—22no—
1067C22×C3—21no—
1068C22×C3—21no—
1069C22×C3—21no—
1070C22×C3—21no—
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—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3—41no—
1086C22×C3—41no—
1087C22×C3—42no—
1088C22×C3—41no—
1089C22×C3—62no—
1090C22×C3—61no—
1091C22×C3—61no—
1092C22×C3—61no—
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—81no—
1103C22×C3—81no—
1104C22×C3—92no—
1105C22×C3—121no—
1106C22×C3—121no—
1107C22×C3—121no—
1108C22×C3—121no—
1109C22×C3—121no—
1110C22×C3—181no—
1111C22×C3—181no—
1112C22×C3—181no—
1113C22×C3—181no—
1114C22×C3—181no—
1115C22×C3—181no—
1116C22×C3—181no—
1117C22×C3—181no—
1118C22×C3—181no—
1119C22×C3—181no—
1120C22×C3—181no—
1121C22×C3—364no—
1122C22×C3C22×D3211yescharacteristic
1123C22×C3C22×D3211yescharacteristic
1124C22×C3C22×D3211yescharacteristic
1125C2×D3—21no—
1126C2×D3—21no—
1127C2×D3—21no—
1128C2×D3—21no—
1129C2×D3—21no—
1130C2×D3—21no—
1131C2×D3—32no—
1132C2×D3—32no—
1133C2×D3—62no—
1134C2×D3—61no—
1135C2×D3—61no—
1136C2×D3—61no—
1137C2×D3—61no—
1138C2×D3—62no—
1139C2×D3—61no—
1140C2×D3—61no—
1141C2×D3—61no—
1142C2×D3—61no—
1143C2×D3—61no—
1144C2×D3—61no—
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—121no—
1158C2×D3—121no—
1159C2×D3—121no—
1160C2×D3—121no—
1161C2×D3—121no—
1162C2×D3—121no—
1163C2×D3—121no—
1164C2×D3—121no—
1165C2×D3—121no—
1166C2×D3—121no—
1167C2×D3—124no—
1168C2×D3—124no—
1169C2×D3—128no—
1170C2×D3—364no—
1171C2×D3—364no—
1172C2×D3—364no—
1173C3×C4—61no—
1174C3×C4—61no—
1175C3×C4—61no—
1176C3×C4—61no—
1177C3×C4—61no—
1178C3×C4—61no—
1179C3×C4—61no—
1180C3×C4—61no—
1181C3×C4—92no—
1182C3×C4—92no—
1183C3×C4—121no—
1184C3×C4—121no—
1185C3×C4—121no—
1186C3×C4—121no—
1187Dic3—21no—
1188Dic3—21no—
1189Dic3—21no—
1190Dic3—21no—
1191Dic3—32no—
1192Dic3—32no—
1193Dic3—32no—
1194Dic3—32no—
1195Dic3—62no—
1196Dic3—62no—
1197Dic3—181no—
1198Dic3—181no—
1199Dic3—181no—
1200Dic3—181no—
1201Dic3—181no—
1202Dic3—181no—
1203Dic3—361no—
1204Dic3—361no—
1205Dic3—361no—
1206Dic3—361no—
1207Dic3—361no—
1208Dic3—361no—
1209Dic3—721no—
1210Dic3—721no—
1211C32—21no—
1212C32—21no—
1213C32—21no—
1214C32—41no—
1215C32#559211yescharacteristic, complemented
1216C32#560711yescharacteristic, complemented
1217C32#571511yescharacteristic, complemented
1218C23—31no—
1219C23—31no—
1220C23—91no—
1221C23—91no—
1222C23—91no—
1223C23—91no—
1224C23—182no—
1225C23—361no—
1226C23—361no—
1227C23—542no—
1228C23—1081no—
1229C23—1081no—
1230C23D3311yescharacteristic
1231Q8—542no—
1232D4—121no—
1233D4—121no—
1234D4—182no—
1235D4—182no—
1236D4—182no—
1237D4—182no—
1238D4—361no—
1239D4—361no—
1240D4—361no—
1241D4—361no—
1242D4—542no—
1243D4—542no—
1244D4—542no—
1245D4—1081no—
1246D4—1081no—
1247C2×C4—31no—
1248C2×C4—31no—
1249C2×C4—31no—
1250C2×C4—31no—
1251C2×C4—91no—
1252C2×C4—91no—
1253C2×C4—182no—
1254C2×C4—274no—
1255C2×C4—271no—
1256C2×C4—271no—
1257C2×C4—542no—
1258C2×C3—21no—
1259C2×C3—21no—
1260C2×C3—21no—
1261C2×C3—21no—
1262C2×C3—21no—
1263C2×C3—21no—
1264C2×C3—21no—
1265C2×C3—21no—
1266C2×C3—21no—
1267C2×C3—42no—
1268C2×C3—41no—
1269C2×C3—41no—
1270C2×C3—41no—
1271C2×C3—41no—
1272C2×C3—41no—
1273C2×C3—41no—
1274C2×C3—81no—
1275C2×C3—81no—
1276C2×C3—82no—
1277C2×C3—122no—
1278C2×C3—121no—
1279C2×C3—121no—
1280C2×C3—121no—
1281C2×C3—121no—
1282C2×C3—182no—
1283C2×C3—241no—
1284C2×C3—361no—
1285C2×C3—361no—
1286C2×C3—361no—
1287C2×C3#6430711yescharacteristic
1288C2×C3D32×D411yescharacteristic
1289C2×C3D32×D411yescharacteristic
1290C2×C3D32×D411yescharacteristic
1291C2×C3#6431311yescharacteristic
1292C2×C3#6431311yescharacteristic
1293C2×C3#6431411yescharacteristic
1294C2×C3#6433011yescharacteristic
1295C2×C3#6433011yescharacteristic
1296D3—41no—
1297D3—41no—
1298D3—62no—
1299D3—62no—
1300D3—122no—
1301D3—122no—
1302D3—121no—
1303D3—121no—
1304D3—121no—
1305D3—121no—
1306D3—121no—
1307D3—121no—
1308D3—241no—
1309D3—241no—
1310C22—21no—
1311C22—21no—
1312C22—21no—
1313C22—61no—
1314C22—61no—
1315C22—61no—
1316C22—61no—
1317C22—61no—
1318C22—61no—
1319C22—92no—
1320C22—181no—
1321C22—181no—
1322C22—181no—
1323C22—181no—
1324C22—181no—
1325C22—181no—
1326C22—181no—
1327C22—181no—
1328C22—181no—
1329C22—181no—
1330C22—181no—
1331C22—364no—
1332C22—1084no—
1333C22C2×D3311yescharacteristic
1334C4—61no—
1335C4—61no—
1336C4—61no—
1337C4—61no—
1338C4—92no—
1339C4—92no—
1340C4—541no—
1341C4—541no—
1342C3—21no—
1343C3—21no—
1344C3—21no—
1345C3—41no—
1346C3#1059426911yescharacteristic, complemented
1347C3#1059528611yescharacteristic, complemented
1348C3#1059529911yescharacteristic, complemented
1349C2—41no—
1350C2—121no—
1351C2—121no—
1352C2—182no—
1353C2—361no—
1354C2—361no—
1355C2—361no—
1356C2#1172441511yescharacteristic
1357C2#1172441811yescharacteristic
1358C2#1172444011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#535
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×#88961C2semidirect
3. #11723634C2semidirect
4. #11723615C2semidirect
5. #11723591C2semidirect
6. C3×#63981C2semidirect
7. C3×#63979C2semidirect
8. C3×#63971C2semidirect
9. #11723029C2semidirect
10. #11723010C2semidirect
11. #11722960C2semidirect
12. #11722955C2semidirect
13. #11722951C2semidirect
14. #11722951C2semidirect
15. #11722922C2semidirect
23. C2×C32×#67C22semidirect
24. C2×C32×#67C22semidirect
29. C2×#6293C22semidirect
31. C2×#6290C22semidirect
32. C2×#6290C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#626C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#626C22semidirect
39. C2×C3×#625C22semidirect
40. C2×C3×D3×Dic3C22semidirect
42. #88864C22semidirect
43. C32×#217C22semidirect
44. #88807C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. #88803C22semidirect
49. #88803C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. C3×#3724C22semidirect
53. C3×#3722C22semidirect
54. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
73. #63981D3semidirect
77. #63979D3semidirect
82. #63971D3semidirect
131. #6294D4semidirect
178. C2×C3×#67C2×D3semidirect
179. C2×C3×#67C2×D3semidirect
180. C2×C3×#67C2×D3semidirect
181. C2×C3×#67C2×D3semidirect
200. C2×#626C2×D3semidirect
201. C2×#626C2×D3semidirect
202. C2×#626C2×D3semidirect
203. C2×#626C2×D3semidirect
215. C2×#625C2×D3semidirect
224. C2×D3×Dic3C2×D3semidirect
242. C3×#217C2×D3semidirect
243. C3×#217C2×D3semidirect
254. #3724C2×D3semidirect
259. #3722C2×D3semidirect
260. #3722C2×D3semidirect
279. Dic32C2×D3semidirect
579. C2×#67D32semidirect
580. C2×#67D32semidirect
626. #217D32semidirect
820. C33#535semidirect
1215. C32#5592semidirect
1216. C32#5607semidirect
1217. C32#5715semidirect
1346. C3#10594269semidirect
1347. C3#10595286semidirect
1348. C3#10595299semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#889612
#117236342
#117236152
#117235912
C3×#639812
C3×#639792
C3×#639712
#117230292
#117230102
#117229602
#117229552
#117229512
#117229222
#105952993
#105952863
#105942693