Finite Group Databasebeta

← #13169376

Subgroups — #13169376

Order 1728.

1064 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2#11723427C211yesmaximal, characteristic, complemented
3#11723407C211yesmaximal, characteristic, complemented
4#11723389C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×#63880C211yesmaximal, characteristic
7C3×#63858C211yesmaximal, characteristic, complemented
8#11723001C211yesmaximal, characteristic
9#11723001C211yesmaximal, characteristic
10#11722972C211yesmaximal, characteristic, complemented
11#11722971C211yesmaximal, characteristic, complemented
12#11722941C211yesmaximal, characteristic, complemented
13#11722940C211yesmaximal, characteristic, complemented
14#11722915C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10594450—31nomaximal
17#10594248—31nomaximal
18#10593863—31nomaximal
19C2×#6293C2211yescharacteristic
20C2×C3×#627C2211yescharacteristic
21C2×C3×#627C2211yescharacteristic
22C2×C3×#626C2211yescharacteristic
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25#88857C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×C4×Dic3C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64107—31no—
55#64088—31no—
56C4×#634—31no—
57C3×#898—31no—
58C3×#888—31no—
59C3×#67⋊C4—31no—
60C3×#879—31no—
61C3×C4×D12—31no—
62C3×#869—31no—
63#63964—31no—
64#63959—31no—
65#63959—31no—
66#63955—31no—
67#63918D311yescharacteristic, complemented
68#63907—31no—
69#63907—31no—
70#63895—31no—
71#63893—31no—
72#63880D311yescharacteristic
73#63878—31no—
74#63863—31no—
75#63863—31no—
76#63861—31no—
77#63858—31no—
78#63858—31no—
79#63858—31no—
80#63858—31no—
81#63858—31no—
82#63858—61no—
83#63858—61no—
84#63858D311yescharacteristic, complemented
85#63857—31no—
86#63857—31no—
87#63855—31no—
88#63851—31no—
89#63848—31no—
90#63843—31no—
91#63843—31no—
92#63843—31no—
93Dic3×Dic6—31no—
94#63841—31no—
95#63841—31no—
96#63838—31no—
97#63837—31no—
98#63837—31no—
99#63837—31no—
100#63837—61no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6293—22no—
118C3×#627—22no—
119C3×#627—22no—
120C3×#626—22no—
121C3×#624—22no—
122C3×D3×Dic3—22no—
123#5732—91no—
124#5702—91no—
125#5542—91no—
126C2×#634—31no—
127C2×C3×#67—31no—
128C22×C3×Dic3—31no—
129C2×C3×D12—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#627—61no—
140C2×#627C2×D311yescharacteristic
141C2×#627C2×D311yescharacteristic
142C2×#626C2×D311yescharacteristic
143C2×#624C2×D311yescharacteristic
144C2×D3×Dic3C2×D311yescharacteristic
145C32×C4⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C42—31no—
148#3757—31no—
149#3757—31no—
150#3752—31no—
151#3752—31no—
152#3752C2×D311yescharacteristic
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)C2×D311yescharacteristic
156#3750—31no—
157#3750—31no—
158#3750—31no—
159#3750—31no—
160#3750—61no—
161#3750—61no—
162#3750—61no—
163#3750—121no—
164#3750C2×D311yescharacteristic
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×#217—31no—
170C3×#217—31no—
171C3×(C2×D3)⋊C4—21no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—61no—
177C3×(C2×D3)⋊C4C2×D311yescharacteristic
178C3×(C2×D3)⋊C4C2×D311yescharacteristic
179C3×C4⋊Dic3—21no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—61no—
187C3×C4⋊Dic3C2×D311yescharacteristic
188C3×C4⋊Dic3C2×D311yescharacteristic
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—61no—
196C3×C4×Dic3—21no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3C2×D311yescharacteristic
200C3×C4×Dic3C2×D311yescharacteristic
201#3724—31no—
202Dic3⋊Dic3—31no—
203Dic3⋊Dic3—31no—
204Dic3⋊Dic3—31no—
205Dic3⋊Dic3—31no—
206Dic3⋊Dic3—31no—
207Dic3⋊Dic3—31no—
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—61no—
211Dic3⋊Dic3—61no—
212Dic3⋊Dic3—61no—
213Dic3⋊Dic3C2×D311yescharacteristic
214Dic3⋊Dic3C2×D311yescharacteristic
215Dic3⋊Dic3C2×D311yescharacteristic
216Dic3⋊Dic3C2×D311yescharacteristic
217#3722—31no—
218#3722—31no—
219(C2×D3)⋊Dic3—31no—
220(C2×D3)⋊Dic3—31no—
221(C2×D3)⋊Dic3—31no—
222(C2×D3)⋊Dic3—31no—
223(C2×D3)⋊Dic3—31no—
224(C2×D3)⋊Dic3—31no—
225(C2×D3)⋊Dic3—31no—
226(C2×D3)⋊Dic3—31no—
227(C2×D3)⋊Dic3—31no—
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—61no—
232(C2×D3)⋊Dic3—61no—
233(C2×D3)⋊Dic3—61no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3C2×D311yescharacteristic
236(C2×D3)⋊Dic3C2×D311yescharacteristic
237Dic32—31no—
238Dic32—31no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—61no—
249Dic32—61no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3×C3⋊D3—21no—
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3⋊(C3⋊Dic3)—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3#4112yes—
272C32×Dic3#4112yes—
273C3×C4⋊Q8—91no—
274C3×#126—91no—
275C3×C4×D4—91no—
276#947—91no—
277#947—91no—
278Q8×Dic3—91no—
279Q8×Dic3—91no—
280#936—91no—
281#936—91no—
282#926—91no—
283#926—91no—
284#924—91no—
285#924—91no—
286#898—31no—
287#898—91no—
288#898—91no—
289#898—91no—
290#898—91no—
291#898—91no—
292#898—181no—
293#897—91no—
294#897—91no—
295#896—91no—
296#892—91no—
297#892—91no—
298#888—31no—
299#887—91no—
300#887—91no—
301#887—91no—
302#887—91no—
303#885—91no—
304#885—91no—
305#67⋊C4—31no—
306#879—31no—
307#879—91no—
308#879—91no—
309#879—91no—
310#879—91no—
311#879—181no—
312#878—91no—
313#877—91no—
314C4×D12—31no—
315#872—91no—
316#869—31no—
317C4×Dic6—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C4×Dic6—181no—
321C23×C32—31no—
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—21no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—61no—
327C22×C3×D3C22×D311yescharacteristic
328C22×C3×D3C22×D311yescharacteristic
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—41no—
338C2×C32×C4C22×D311yescharacteristic
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—121no—
354C2×C3⋊Dic3—121no—
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360#634—62no—
361C3×#67—62no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—62no—
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C3×D12—62no—
394C3×C4×D3—62no—
395C3×C4×D3—62no—
396C3×C4×D3—62no—
397C3×Dic6—62no—
398C3×Dic6—62no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401#627—22no—
402#627—22no—
403#627—64no—
404#627—62no—
405#627—62no—
406#626—22no—
407#624—22no—
408D3×Dic3—22no—
409#556—271noSylow
410C2×C33C2×#4111yescharacteristic
411C2×C33C2×#4111yescharacteristic
412C2×C332−1+411yescharacteristic
413C3×C3⋊D3—41no—
414C32×D3—41no—
415C2×C3×Q8—91no—
416C2×C3×Q8—91no—
417C2×C3×D4—91no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C2×#67—31no—
421C22×Dic3—31no—
422C2×D12—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×Dic6—31no—
427C2×Dic6—31no—
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6—91no—
431C2×Dic6—91no—
432C2×Dic6—91no—
433C2×Dic6—181no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—61no—
437C3×C4⋊C4—91no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C22⋊C4—31no—
444C3×C22⋊C4—31no—
445C3×C22⋊C4—61no—
446C3×C22⋊C4—91no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C42—31no—
450C3×C42—31no—
451C3×C42—61no—
452C3×C42—91no—
453#217—31no—
454#217—31no—
455#217—91no—
456#217—91no—
457#217—91no—
458#217—91no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—91no—
463#217—181no—
464#217—181no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
469(C2×D3)⋊C4—61no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—181no—
481(C2×D3)⋊C4—181no—
482(C2×D3)⋊C4D3211yescharacteristic
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—61no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—181no—
497C4⋊Dic3—181no—
498C4⋊Dic3D3211yescharacteristic
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—61no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—181no—
516Dic3⋊C4—181no—
517Dic3⋊C4—181no—
518Dic3⋊C4—181no—
519Dic3⋊C4—361no—
520C4×Dic3—31no—
521C4×Dic3—31no—
522C4×Dic3—91no—
523C4×Dic3—91no—
524C4×Dic3—91no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C4×Dic3—91no—
528C4×Dic3—91no—
529C4×Dic3—91no—
530C4×Dic3—91no—
531C4×Dic3—91no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—181no—
538C4×Dic3—181no—
539C4×Dic3—181no—
540C4×Dic3—181no—
541C4×Dic3D3211yescharacteristic
542C22×C32—21no—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—41no—
546C22×C32—61no—
547C22×C32—61no—
548C22×C32—61no—
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C22×C32C23×D311yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3×D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—21no—
560C2×C3×D3—21no—
561C2×C3×D3—41no—
562C2×C3×D3—41no—
563C2×C3×D3—41no—
564C2×C3×D3—61no—
565C2×C3×D3—61no—
566C2×C3×D3—61no—
567C2×C3×D3—61no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—121no—
571C2×C3×D3—121no—
572C2×C3×D3—121no—
573C32×C4—21no—
574C32×C4—21no—
575C32×C4—21no—
576C32×C4—32no—
577C32×C4—32no—
578C32×C4—41no—
579C32×C4—41no—
580C32×C4—41no—
581C32×C4—61no—
582C32×C4—61no—
583C32×C4—61no—
584C32×C4—81no—
585C3⋊Dic3—21no—
586C3⋊Dic3—21no—
587C3⋊Dic3—21no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—61no—
591C3⋊Dic3—62no—
592C3⋊Dic3—61no—
593C3⋊Dic3—61no—
594C3⋊Dic3—61no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—121no—
598C3⋊Dic3—121no—
599C3⋊Dic3—122no—
600C3⋊Dic3—121no—
601C3⋊Dic3—121no—
602C3⋊Dic3—121no—
603C3⋊Dic3—241no—
604C3×Dic3—21no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—22no—
611C3×Dic3—22no—
612C3×Dic3—41no—
613C3×Dic3—41no—
614C3×Dic3—41no—
615C3×Dic3—62no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—121no—
627C3×Dic3—121no—
628C3×Dic3—121no—
629C3×Dic3—121no—
630C3×Dic3#23512yes—
631C3×Dic3#23712yes—
632C3×Dic3#23712yes—
633C3×Dic3#23912yes—
634C4⋊Q8—91no—
635#126—91no—
636#126—271no—
637#126—271no—
638#126—271no—
639#124—271no—
640#124—271no—
641C22⋊Q8—271no—
642C22⋊Q8—271no—
643C4×Q8—271no—
644C4×Q8—271no—
645C4×Q8—271no—
646C4×D4—91no—
647#117—271no—
648#117—271no—
649C33#55611yescharacteristic, complemented, Sylow
650C23×C3—31no—
651C23×C3—31no—
652C23×C3—61no—
653C23×C3—91no—
654C22×D3—31no—
655C22×D3—31no—
656C22×D3—61no—
657C22×D3C2×D3211yescharacteristic
658C3×Q8—182no—
659C3×Q8—182no—
660C3×D4—182no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—41no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—91no—
681C2×C3×C4—91no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—182no—
686C2×C3×C4—182no—
687C2×C3×C4C2×D3211yescharacteristic
688C2×C3×C4C2×D3211yescharacteristic
689C2×C3×C4C2×D3211yescharacteristic
690#67—62no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—62no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—91no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—361no—
720C2×Dic3—361no—
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726D12—62no—
727C4×D3—62no—
728C4×D3—62no—
729C4×D3—62no—
730Dic6—62no—
731Dic6—62no—
732Dic6—62no—
733Dic6—62no—
734Dic6—182no—
735Dic6—182no—
736Dic6—184no—
737Dic6—182no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—121no—
751C2×C32C2×#23511yescharacteristic
752C2×C32C2×#23711yescharacteristic
753C2×C32C2×#23711yescharacteristic
754C2×C32C2×#23911yescharacteristic
755C2×C32#100711yescharacteristic
756C2×C32D3×#4111yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32#101011yescharacteristic
759C2×C32#101011yescharacteristic
760C3⋊D3—41no—
761C3×D3—41no—
762C3×D3—41no—
763C3×D3—81no—
764C3×D3—121no—
765C3×D3—121no—
766C3×D3—241no—
767C2×Q8—91no—
768C2×Q8—91no—
769C2×Q8—271no—
770C2×D4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C4⋊C4—31no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—271no—
781C4⋊C4—271no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C22⋊C4—31no—
786C22⋊C4—91no—
787C22⋊C4—91no—
788C22⋊C4—91no—
789C22⋊C4—271no—
790C22⋊C4—271no—
791C22⋊C4—271no—
792C22⋊C4—271no—
793C22⋊C4—271no—
794C22⋊C4—271no—
795C42—31no—
796C42—91no—
797C42—271no—
798C42—271no—
799C42—271no—
800C42—271no—
801C42—271no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—41no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—181no—
816C22×C3—181no—
817C22×C3—181no—
818C22×C3C22×D3211yescharacteristic
819C22×C3C22×D3211yescharacteristic
820C22×C3C22×D3211yescharacteristic
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—32no—
837C3×C4—32no—
838C3×C4—32no—
839C3×C4—32no—
840C3×C4—41no—
841C3×C4—41no—
842C3×C4—41no—
843C3×C4—62no—
844C3×C4—62no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—81no—
852C3×C4—121no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4—181no—
856C3×C4—181no—
857C3×C4—181no—
858C3×C4—181no—
859C3×C4—181no—
860Dic3—21no—
861Dic3—21no—
862Dic3—21no—
863Dic3—62no—
864Dic3—61no—
865Dic3—61no—
866Dic3—61no—
867Dic3—61no—
868Dic3—61no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—121no—
875Dic3—121no—
876Dic3—121no—
877Dic3—121no—
878Dic3—182no—
879Dic3—181no—
880Dic3—181no—
881Dic3—181no—
882Dic3—181no—
883Dic3—181no—
884Dic3—181no—
885Dic3—361no—
886Dic3—361no—
887Dic3—361no—
888Dic3—361no—
889Dic3—361no—
890Dic3—362no—
891Dic3—721no—
892Dic3#379512yes—
893Dic3#379612yes—
894C32—21no—
895C32—21no—
896C32—21no—
897C32—41no—
898C32#554211yescharacteristic, complemented
899C32#570211yescharacteristic, complemented
900C32#573211yescharacteristic, complemented
901C23—31no—
902C23—91no—
903Q8—182no—
904Q8—182no—
905Q8—542no—
906D4—182no—
907C2×C4—31no—
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—91no—
913C2×C4—91no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—182no—
918C2×C4—182no—
919C2×C4—271no—
920C2×C4—271no—
921C2×C4D3311yescharacteristic
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—41no—
932C2×C3—41no—
933C2×C3—41no—
934C2×C3—121no—
935C2×C3—121no—
936C2×C3—241no—
937C2×C3—361no—
938C2×C3C2×#379511yescharacteristic
939C2×C3C2×#379611yescharacteristic
940C2×C3#6429711yescharacteristic
941C2×C3#6429711yescharacteristic
942C2×C3D3×#23511yescharacteristic
943C2×C3#6430911yescharacteristic
944C2×C3D3×#23711yescharacteristic
945C2×C3D3×#23711yescharacteristic
946C2×C3D3×#23911yescharacteristic
947D3—41no—
948D3—121no—
949D3—121no—
950D3—241no—
951C22—61no—
952C22—61no—
953C22—61no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22C2×D3311yescharacteristic
958C4—21no—
959C4—32no—
960C4—32no—
961C4—61no—
962C4—61no—
963C4—61no—
964C4—181no—
965C4—181no—
966C4—181no—
967C4—181no—
968C4—181no—
969C4—541no—
970C4—541no—
971C3—21no—
972C3—21no—
973C3—21no—
974C3—41no—
975C3#1059386311yescharacteristic, complemented
976C3#1059424811yescharacteristic, complemented
977C3#1059445011yescharacteristic, complemented
978C2—121no—
979C2—361no—
980C2D3×#379511yescharacteristic
981C2D3×#379611yescharacteristic
982C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#626C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723675C2semidirect
2. #11723427C2semidirect
3. #11723407C2semidirect
4. #11723389C2semidirect
5. C3×#63918C2semidirect
7. C3×#63858C2semidirect
10. #11722972C2semidirect
11. #11722971C2semidirect
12. #11722941C2semidirect
13. #11722940C2semidirect
14. #11722915C2semidirect
15. #11722914C2semidirect
67. #63918D3semidirect
84. #63858D3semidirect
649. C33#556semidirect
898. C32#5542semidirect
899. C32#5702semidirect
900. C32#5732semidirect
975. C3#10593863semidirect
976. C3#10594248semidirect
977. C3#10594450semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117234272
#117234072
#117233892
C3×#639182
C3×#638802
C3×#638582
#117230012
#117229722
#117229712
#117229412
#117229402
#117229152
#117229142
#105944503
#105942483
#105938633