Finite Group Databasebeta

← #13169361

Subgroups — #13169361

Order 1728.

1136 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723679C211yesmaximal, characteristic, complemented
2#11723510C211yesmaximal, characteristic
3#11723469C211yesmaximal, characteristic, complemented
4#11723468C211yesmaximal, characteristic, complemented
5C3×#63867C211yesmaximal, characteristic, complemented
6C3×#63855C211yesmaximal, characteristic, complemented
7C3×#63851C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11723019C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11722996C211yesmaximal, characteristic
12#11722996C211yesmaximal, characteristic
13#11722973C211yesmaximal, characteristic, complemented
14#11722941C211yesmaximal, characteristic, complemented
15#11722912C211yesmaximal, characteristic, complemented
16#10594970—31nomaximal
17#10594334—31nomaximal
18#10593872—31nomaximal
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6291C2211yescharacteristic
21C2×#6289C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25#88859C2211yescharacteristic
26C3×#3750C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88807C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37#88804C2211yescharacteristic
38#88804C2211yescharacteristic
39(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C4×#638—31no—
55#64101—31no—
56#64081—31no—
57C3×#926—31no—
58C3×#924—31no—
59C3×#896—31no—
60C3×#889—31no—
61C3×#872—31no—
62C3×#870—31no—
63#63975—31no—
64#63975—31no—
65#63956—31no—
66#63956—31no—
67#63904—31no—
68#63904—31no—
69#63904—61no—
70#63900—31no—
71#63895—31no—
72#63888—31no—
73#63883—31no—
74#63883—31no—
75#63872—31no—
76#63871—31no—
77#63870—31no—
78#63867—31no—
79#63867—31no—
80#63867D311yescharacteristic, complemented
81#63862—31no—
82#63862—31no—
83#63861—31no—
84#63858—31no—
85#63855D311yescharacteristic, complemented
86#63854—31no—
87#63854—31no—
88#63853—31no—
89#63853—31no—
90#63851D311yescharacteristic, complemented
91#63846—31no—
92#63845—31no—
93#63843—31no—
94#63843—31no—
95#63838—31no—
96#63836—31no—
97#63836—31no—
98#63836—31no—
99#63836—31no—
100#63836—61no—
101#63836—61no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
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
117C32×C4×D3—22no—
118#6291—22no—
119#6289—22no—
120#6289—22no—
121#6289—22no—
122C3×#627—22no—
123#5693—91no—
124#5639—91no—
125#5529—91no—
126C22×C32×C4—31no—
127C2×#638—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—31no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×#627C2×D311yescharacteristic
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—61no—
140C2×#624—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×#624—31no—
144C2×#624—31no—
145C2×#624—31no—
146C2×#624—61no—
147C2×#624—61no—
148C2×#624—61no—
149C32×C4⋊C4—31no—
150C32×C42—31no—
151#3757—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—61no—
158#3752—61no—
159#3752—61no—
160#3752—121no—
161C4⋊(C3⋊Dic3)—31no—
162#3750—31no—
163#3750C2×D311yescharacteristic
164#3750C2×D311yescharacteristic
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3C2×D311yescharacteristic
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×Dic3⋊C4—21no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
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—31no—
196C3×Dic3⋊C4—61no—
197C3×Dic3⋊C4—61no—
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×Dic3⋊C4C2×D311yescharacteristic
200C3×C4×Dic3—21no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—61no—
204C3×C4×Dic3C2×D311yescharacteristic
205C3×C4×Dic3C2×D311yescharacteristic
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724C2×D311yescharacteristic
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—61no—
236#3722—61no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—61no—
240(C2×D3)⋊Dic3C2×D311yescharacteristic
241(C2×D3)⋊Dic3C2×D311yescharacteristic
242(C2×D3)⋊Dic3C2×D311yescharacteristic
243(C2×D3)⋊Dic3C2×D311yescharacteristic
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32—61no—
252Dic32—61no—
253C22×C33C2411yescharacteristic
254C2×C3⋊(C3⋊D3)—21no—
255C2×C3⋊(C3⋊D3)—21no—
256C2×C3⋊(C3⋊D3)#4112yes—
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—21no—
272C32×Dic3#4112yes—
273C3×#125—91no—
274C3×C22⋊Q8—91no—
275C3×#117—91no—
276#946—91no—
277Q8×Dic3—91no—
278C4×#67—91no—
279C4×#67—91no—
280C4×#67—181no—
281#926—31no—
282#924—31no—
283#898—91no—
284#898—91no—
285#897—91no—
286#896—31no—
287#896—91no—
288#894—91no—
289#894—91no—
290#893—91no—
291#892—91no—
292#892—91no—
293#892—91no—
294#892—181no—
295D3×C4⋊C4—91no—
296D3×C4⋊C4—91no—
297D3×C4⋊C4—91no—
298#890—91no—
299#890—91no—
300#889—31no—
301#889—91no—
302#889—91no—
303#889—91no—
304#887—91no—
305#887—91no—
306#883—91no—
307#883—91no—
308#883—91no—
309#883—91no—
310#879—91no—
311#879—91no—
312#879—91no—
313#879—91no—
314#872—31no—
315#872—91no—
316#872—91no—
317#872—91no—
318#872—181no—
319#870—31no—
320#870—91no—
321C23×C32—31no—
322C22×C3⋊D3—31no—
323C22×C3⋊D3—31no—
324C22×C3⋊D3—31no—
325C22×C3⋊D3—61no—
326C22×C3⋊D3—61no—
327C22×C3⋊D3—61no—
328C22×C3⋊D3—121no—
329C22×C3×D3—21no—
330C22×C3×D3C22×D311yescharacteristic
331C22×C3×D3C22×D311yescharacteristic
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—41no—
341C2×C32×C4—62no—
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345#638—62no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—31no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—121no—
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C4×C3⋊D3—62no—
360C4×C3⋊D3—62no—
361C4×C3⋊D3—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—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
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
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C3×C4×D3—22no—
396C3×C4×D3—22no—
397C3×C4×D3—42no—
398C3×Dic6—62no—
399C3×Dic6—62no—
400#627—22no—
401#626—62no—
402#626—62no—
403#626—64no—
404#624—62no—
405#624—62no—
406#624—62no—
407#624—62no—
408#624—64no—
409#624—64no—
410#624—62no—
411#624—62no—
412#624—122no—
413#552—271noSylow
414C2×C33C2×#4111yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C332−1+411yescharacteristic
417C3⋊(C3⋊D3)—22no—
418C32×D3—41no—
419C2×C3×Q8—91no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—61no—
423C2×#67—91no—
424C2×#67—91no—
425C2×#67—181no—
426C2×D12—91no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—181no—
437C2×C4×D3—181no—
438C2×C4×D3—181no—
439C2×C4×D3D3211yescharacteristic
440C2×Dic6—31no—
441C2×Dic6—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—61no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C42—31no—
459C3×C42—31no—
460C3×C42—61no—
461C3×C42—91no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—31no—
466#217—91no—
467#217—91no—
468#217—181no—
469(C2×D3)⋊C4—31no—
470(C2×D3)⋊C4—31no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—31no—
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—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—181no—
484(C2×D3)⋊C4—181no—
485(C2×D3)⋊C4—181no—
486(C2×D3)⋊C4—181no—
487(C2×D3)⋊C4—181no—
488(C2×D3)⋊C4—361no—
489C4⋊Dic3—31no—
490C4⋊Dic3—31no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—91no—
498C4⋊Dic3—91no—
499C4⋊Dic3—91no—
500C4⋊Dic3—91no—
501C4⋊Dic3—91no—
502C4⋊Dic3—181no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—61no—
516Dic3⋊C4—61no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—181no—
529Dic3⋊C4D3211yescharacteristic
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—61no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C4×Dic3—181no—
545C4×Dic3D3211yescharacteristic
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—41no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32—61no—
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C22×C32C23×D311yescharacteristic
556C2×C3⋊D3—32no—
557C2×C3⋊D3—32no—
558C2×C3⋊D3—32no—
559C2×C3⋊D3—62no—
560C2×C3⋊D3—62no—
561C2×C3⋊D3—62no—
562C2×C3⋊D3—61no—
563C2×C3⋊D3—61no—
564C2×C3⋊D3—61no—
565C2×C3⋊D3—61no—
566C2×C3⋊D3—61no—
567C2×C3⋊D3—61no—
568C2×C3⋊D3—122no—
569C2×C3⋊D3—121no—
570C2×C3⋊D3—121no—
571C2×C3⋊D3—121no—
572C2×C3⋊D3—121no—
573C2×C3⋊D3—121no—
574C2×C3⋊D3—121no—
575C2×C3⋊D3—241no—
576C2×C3⋊D3—241no—
577C2×C3×D3—22no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—21no—
584C2×C3×D3—41no—
585C2×C3×D3—41no—
586C32×C4—21no—
587C32×C4—21no—
588C32×C4—21no—
589C32×C4—32no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—41no—
593C32×C4—61no—
594C32×C4—61no—
595C32×C4—61no—
596C32×C4—61no—
597C32×C4—81no—
598C3⋊Dic3—21no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—61no—
605C3⋊Dic3—61no—
606C3⋊Dic3—61no—
607C3⋊Dic3—121no—
608C3⋊Dic3—121no—
609C3⋊Dic3—121no—
610C3⋊Dic3—241no—
611C3×Dic3—22no—
612C3×Dic3—22no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—21no—
621C3×Dic3—22no—
622C3×Dic3—41no—
623C3×Dic3—41no—
624C3×Dic3—62no—
625C3×Dic3—62no—
626C3×Dic3—62no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—61no—
638C3×Dic3—61no—
639C3×Dic3—121no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642C3×Dic3#23512yes—
643C3×Dic3#23712yes—
644#126—271no—
645#126—271no—
646#125—91no—
647#125—271no—
648#125—271no—
649#123—271no—
650#123—271no—
651C22⋊Q8—91no—
652C22⋊Q8—271no—
653C4×Q8—271no—
654C4×D4—271no—
655#117—91no—
656#117—271no—
657#117—271no—
658C2×C4⋊C4—271no—
659C33#55211yescharacteristic, complemented, Sylow
660C23×C3—31no—
661C23×C3—31no—
662C23×C3—61no—
663C22×D3—91no—
664C22×D3—91no—
665C22×D3—91no—
666C22×D3—181no—
667C22×D3—181no—
668C22×D3—181no—
669C22×D3—361no—
670C22×D3C2×D3211yescharacteristic
671C3×Q8—182no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—31no—
684C2×C3×C4—31no—
685C2×C3×C4—41no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—62no—
692C2×C3×C4—62no—
693C2×C3×C4—91no—
694C2×C3×C4—91no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—91no—
699C2×C3×C4—122no—
700C2×C3×C4C2×D3211yescharacteristic
701C2×C3×C4C2×D3211yescharacteristic
702C2×C3×C4C2×D3211yescharacteristic
703#67—182no—
704#67—182no—
705#67—184no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—91no—
725C2×Dic3—91no—
726C2×Dic3—91no—
727C2×Dic3—181no—
728C2×Dic3—181no—
729C2×Dic3—181no—
730C2×Dic3—361no—
731C2×Dic3C2×D3211yescharacteristic
732C2×Dic3C2×D3211yescharacteristic
733C2×Dic3C2×D3211yescharacteristic
734C2×Dic3C2×D3211yescharacteristic
735C2×Dic3C2×D3211yescharacteristic
736D12—182no—
737C4×D3—22no—
738C4×D3—182no—
739C4×D3—182no—
740C4×D3—182no—
741C4×D3—182no—
742C4×D3—182no—
743C4×D3—182no—
744C4×D3—182no—
745C4×D3—182no—
746C4×D3—184no—
747C4×D3—184no—
748C4×D3—182no—
749C4×D3—362no—
750Dic6—62no—
751Dic6—62no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—21no—
760C2×C32—21no—
761C2×C32—41no—
762C2×C32—41no—
763C2×C32—41no—
764C2×C32—121no—
765C2×C32C2×#23511yescharacteristic
766C2×C32C2×#23711yescharacteristic
767C2×C32#100711yescharacteristic
768C2×C32#100711yescharacteristic
769C2×C32D3×#4111yescharacteristic
770C2×C32D3×#4111yescharacteristic
771C2×C32D3×#4111yescharacteristic
772C2×C32D3×#4111yescharacteristic
773C2×C32#101011yescharacteristic
774C3⋊D3—62no—
775C3⋊D3—62no—
776C3⋊D3—62no—
777C3⋊D3—122no—
778C3⋊D3—122no—
779C3⋊D3—122no—
780C3⋊D3—242no—
781C3×D3—42no—
782C3×D3—41no—
783C3×D3—41no—
784C2×Q8—91no—
785C2×D4—271no—
786C22×C4—31no—
787C22×C4—271no—
788C22×C4—271no—
789C22×C4—271no—
790C4⋊C4—31no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4—91no—
794C4⋊C4—91no—
795C4⋊C4—91no—
796C4⋊C4—91no—
797C4⋊C4—91no—
798C4⋊C4—91no—
799C4⋊C4—91no—
800C4⋊C4—271no—
801C4⋊C4—271no—
802C4⋊C4—271no—
803C4⋊C4—271no—
804C4⋊C4—271no—
805C4⋊C4—271no—
806C22⋊C4—91no—
807C22⋊C4—91no—
808C22⋊C4—91no—
809C22⋊C4—91no—
810C22⋊C4—271no—
811C22⋊C4—271no—
812C22⋊C4—271no—
813C22⋊C4—271no—
814C42—31no—
815C42—91no—
816C42—271no—
817C42—271no—
818C42—271no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—41no—
823C22×C3—62no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—61no—
827C22×C3—61no—
828C22×C3—61no—
829C22×C3—61no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3C22×D3211yescharacteristic
833C22×C3C22×D3211yescharacteristic
834C22×C3C22×D3211yescharacteristic
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—92no—
839C2×D3—92no—
840C2×D3—92no—
841C2×D3—182no—
842C2×D3—182no—
843C2×D3—182no—
844C2×D3—181no—
845C2×D3—181no—
846C2×D3—181no—
847C2×D3—181no—
848C2×D3—181no—
849C2×D3—181no—
850C2×D3—362no—
851C2×D3—361no—
852C2×D3—361no—
853C2×D3—361no—
854C2×D3—361no—
855C2×D3—361no—
856C2×D3—361no—
857C2×D3—721no—
858C2×D3—721no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—32no—
863C3×C4—32no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—61no—
871C3×C4—61no—
872C3×C4—61no—
873C3×C4—61no—
874C3×C4—61no—
875C3×C4—61no—
876C3×C4—61no—
877C3×C4—61no—
878C3×C4—81no—
879C3×C4—121no—
880C3×C4—121no—
881C3×C4—181no—
882C3×C4—181no—
883C3×C4—181no—
884C3×C4—181no—
885C3×C4—181no—
886C3×C4—181no—
887Dic3—21no—
888Dic3—21no—
889Dic3—21no—
890Dic3—21no—
891Dic3—62no—
892Dic3—62no—
893Dic3—62no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—61no—
901Dic3—61no—
902Dic3—61no—
903Dic3—61no—
904Dic3—61no—
905Dic3—61no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—181no—
910Dic3—181no—
911Dic3—181no—
912Dic3—361no—
913Dic3—361no—
914Dic3—361no—
915Dic3—721no—
916Dic3#380412yes—
917C32—21no—
918C32—21no—
919C32—21no—
920C32—41no—
921C32#552911yescharacteristic, complemented
922C32#563911yescharacteristic, complemented
923C32#569311yescharacteristic, complemented
924C23—31no—
925C23—271no—
926Q8—182no—
927D4—542no—
928C2×C4—31no—
929C2×C4—31no—
930C2×C4—31no—
931C2×C4—31no—
932C2×C4—31no—
933C2×C4—62no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—91no—
938C2×C4—91no—
939C2×C4—91no—
940C2×C4—271no—
941C2×C4—542no—
942C2×C4—542no—
943C2×C4—542no—
944C2×C4D3311yescharacteristic
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—122no—
958C2×C3—121no—
959C2×C3—121no—
960C2×C3#6429711yescharacteristic
961C2×C3#6429711yescharacteristic
962C2×C3D3×#23511yescharacteristic
963C2×C3#6430611yescharacteristic
964C2×C3#6430611yescharacteristic
965C2×C3#6430611yescharacteristic
966C2×C3D3×#23711yescharacteristic
967C2×C3#6431611yescharacteristic
968C2×C3C2×#380411yescharacteristic
969D3—41no—
970D3—182no—
971D3—182no—
972D3—182no—
973D3—362no—
974D3—362no—
975D3—362no—
976D3—722no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—272no—
981C22—541no—
982C22—541no—
983C22C2×D3311yescharacteristic
984C4—21no—
985C4—32no—
986C4—61no—
987C4—61no—
988C4—61no—
989C4—61no—
990C4—181no—
991C4—181no—
992C4—181no—
993C4—181no—
994C4—181no—
995C4—181no—
996C4—541no—
997C3—21no—
998C3—21no—
999C3—21no—
1000C3—41no—
1001C3#1059387211yescharacteristic, complemented
1002C3#1059433411yescharacteristic, complemented
1003C3#1059497011yescharacteristic, complemented
1004C2—121no—
1005C2—542no—
1006C2#1172439511yescharacteristic
1007C2#1172439811yescharacteristic
1008C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6291C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723679C2semidirect
3. #11723469C2semidirect
4. #11723468C2semidirect
5. C3×#63867C2semidirect
6. C3×#63855C2semidirect
7. C3×#63851C2semidirect
8. #11723022C2semidirect
9. #11723019C2semidirect
10. #11723013C2semidirect
13. #11722973C2semidirect
14. #11722941C2semidirect
15. #11722912C2semidirect
80. #63867D3semidirect
85. #63855D3semidirect
90. #63851D3semidirect
659. C33#552semidirect
921. C32#5529semidirect
922. C32#5639semidirect
923. C32#5693semidirect
1001. C3#10593872semidirect
1002. C3#10594334semidirect
1003. C3#10594970semidirect

Maximal subgroups

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

subgroupindex
#117236792
#117235102
#117234692
#117234682
C3×#638672
C3×#638552
C3×#638512
#117230222
#117230192
#117230132
#117229962
#117229732
#117229412
#117229122
#105949703
#105943343
#105938723