Finite Group Databasebeta

← #13168558

Subgroups — #13168558

Order 1728.

1156 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2#11723470C211yesmaximal, characteristic, complemented
3#11723421C211yesmaximal, characteristic
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63846C211yesmaximal, characteristic, complemented
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723015C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic
11#11722973C211yesmaximal, characteristic, complemented
12#11722940C211yesmaximal, characteristic, complemented
13#11722933C211yesmaximal, characteristic
14#11722920C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10594579—31nomaximal
17#10594469—31nomaximal
18#10594334—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6292C2211yescharacteristic
21C2×#6289C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25C3×#3752C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88803C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64103—31no—
55#64101—31no—
56C4⋊C4×C3⋊D3—31no—
57C3×#897—31no—
58C3×#896—31no—
59C3×#890—31no—
60C3×#890—31no—
61C3×#889—31no—
62C3×#889—31no—
63#63904—31no—
64C4×#626—31no—
65#63897—31no—
66#63895—31no—
67#63895D311yescharacteristic, complemented
68#63894—31no—
69#63888—31no—
70#63883—31no—
71#63883—31no—
72#63883—61no—
73#63871—31no—
74#63870—31no—
75#63862—31no—
76#63861—31no—
77#63858—31no—
78#63858—31no—
79#63855—31no—
80#63854—31no—
81#63853—31no—
82#63853—31no—
83#63853—31no—
84#63853—61no—
85#63849—31no—
86#63849—31no—
87#63849—31no—
88#63849—61no—
89#63848—31no—
90#63848—31no—
91#63846—31no—
92#63846—31no—
93#63846D311yescharacteristic, complemented
94#63845D311yescharacteristic, complemented
95#63843—31no—
96Dic3×Dic6—31no—
97#63841—31no—
98#63837—31no—
99#63836—31no—
100#63836—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C4×C3⋊(C3⋊D3)—22no—
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
117C2×C32×Dic3C2311yescharacteristic
118#6292—22no—
119#6289—22no—
120#6289—22no—
121C3×#627—22no—
122C3×#624—22no—
123#5694—91no—
124#5693—91no—
125#5639—91no—
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—61no—
133C2×C4×C3⋊D3—61no—
134C2×C4×C3⋊D3—61no—
135C2×C4×C3⋊D3—121no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×#627C2×D311yescharacteristic
141C2×#626—31no—
142C2×#626—31no—
143C2×#626—61no—
144C2×#624—31no—
145C2×#624—31no—
146C2×#624—31no—
147C2×#624—31no—
148C2×#624—61no—
149C2×#624—61no—
150C2×#624C2×D311yescharacteristic
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752C2×D311yescharacteristic
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic
161#3750—31no—
162#3750—31no—
163#3750C2×D311yescharacteristic
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—31no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—31no—
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—61no—
171C3×C4⋊Dic3—21no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—61no—
181C3×C4⋊Dic3C2×D311yescharacteristic
182C3×C4⋊Dic3C2×D311yescharacteristic
183C3×Dic3⋊C4—21no—
184C3×Dic3⋊C4—21no—
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—61no—
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×Dic3⋊C4C2×D311yescharacteristic
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×Dic3⋊C4C2×D311yescharacteristic
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204#3724—31no—
205#3724C2×D311yescharacteristic
206Dic3⋊Dic3—31no—
207Dic3⋊Dic3—31no—
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—61no—
215Dic3⋊Dic3—61no—
216Dic3⋊Dic3—61no—
217Dic3⋊Dic3C2×D311yescharacteristic
218Dic3⋊Dic3C2×D311yescharacteristic
219Dic3⋊Dic3C2×D311yescharacteristic
220Dic3⋊Dic3C2×D311yescharacteristic
221Dic3⋊Dic3C2×D311yescharacteristic
222Dic3⋊Dic3C2×D311yescharacteristic
223#3722—31no—
224#3722—31no—
225#3722—31no—
226#3722—31no—
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—61no—
232#3722—61no—
233#3722—61no—
234#3722C2×D311yescharacteristic
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—61no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—61no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3⋊(C3⋊D3)—21no—
255C2×C3⋊(C3⋊D3)—21no—
256C2×C3⋊(C3⋊D3)#4112yes—
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊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—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×#125—91no—
274C3×#125—91no—
275C3×C22⋊Q8—91no—
276#946—91no—
277Q8×Dic3—91no—
278C4×#67—91no—
279#926—91no—
280#898—91no—
281#898—91no—
282#898—91no—
283#898—91no—
284#897—31no—
285#897—91no—
286#896—31no—
287#896—91no—
288#894—91no—
289#894—91no—
290#894—91no—
291#894—91no—
292#894—181no—
293#893—91no—
294#892—91no—
295#892—91no—
296#892—91no—
297#892—91no—
298#892—91no—
299#892—91no—
300#892—181no—
301D3×C4⋊C4—91no—
302D3×C4⋊C4—91no—
303D3×C4⋊C4—91no—
304D3×C4⋊C4—181no—
305#890—31no—
306#890—31no—
307#890—91no—
308#889—31no—
309#889—31no—
310#889—91no—
311#889—91no—
312#887—91no—
313#883—91no—
314#883—91no—
315#879—91no—
316#879—91no—
317C4×D12—91no—
318#872—91no—
319#872—91no—
320C4×Dic6—91no—
321C22×C3⋊D3—31no—
322C22×C3⋊D3—31no—
323C22×C3⋊D3—31no—
324C22×C3⋊D3—61no—
325C22×C3⋊D3—61no—
326C22×C3⋊D3—61no—
327C22×C3⋊D3—121no—
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—61no—
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—31no—
341C2×C32×C4—41no—
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—121no—
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C4⋊(C3⋊D3)—62no—
358C4×C3⋊D3—62no—
359C4×C3⋊D3—62no—
360C4×C3⋊D3—62no—
361C4×C3⋊D3—62no—
362C4×C3⋊D3—62no—
363C4×C3⋊D3—64no—
364C4×C3⋊D3—122no—
365C4×C3⋊D3—122no—
366C4×C3⋊D3—124no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
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—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
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
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C3×C4×D3—62no—
401C3×C4×D3—62no—
402C3×Dic6—62no—
403C3×Dic6—62no—
404#627—22no—
405#626—62no—
406#626—62no—
407#626—122no—
408#624—22no—
409#624—62no—
410#624—62no—
411#624—64no—
412#624—62no—
413#624—62no—
414#624—122no—
415#552—271noSylow
416C2×C33C2×#4111yescharacteristic
417C2×C33C2×#4111yescharacteristic
418C2×C332−1+411yescharacteristic
419C3⋊(C3⋊D3)—22no—
420C3×C3⋊D3—41no—
421C2×C3×Q8—91no—
422C22×C3×C4—91no—
423C2×#67—91no—
424C2×D12—91no—
425C2×D12—91no—
426C2×D12—181no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
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—91no—
437C2×C4×D3—91no—
438C2×C4×D3—181no—
439C2×C4×D3—181no—
440C2×C4×D3—181no—
441C2×C4×D3—181no—
442C2×C4×D3—181no—
443C2×C4×D3—361no—
444C2×Dic6—31no—
445C2×Dic6—31no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—61no—
453C3×C4⋊C4—61no—
454C3×C4⋊C4—61no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C4⋊C4—91no—
458C3×C4⋊C4—91no—
459C3×C4⋊C4—91no—
460C3×C4⋊C4—91no—
461C3×C4⋊C4—91no—
462C3×C4⋊C4—91no—
463C3×C4⋊C4—91no—
464C3×C22⋊C4—91no—
465C3×C22⋊C4—91no—
466C3×C42—91no—
467C3×C42—91no—
468#217—91no—
469#217—91no—
470#217—91no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—31no—
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—61no—
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—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—91no—
488(C2×D3)⋊C4—91no—
489(C2×D3)⋊C4—91no—
490(C2×D3)⋊C4—91no—
491(C2×D3)⋊C4—181no—
492(C2×D3)⋊C4—181no—
493(C2×D3)⋊C4—181no—
494(C2×D3)⋊C4—181no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—31no—
499C4⋊Dic3—31no—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—31no—
503C4⋊Dic3—61no—
504C4⋊Dic3—91no—
505C4⋊Dic3—91no—
506C4⋊Dic3—91no—
507C4⋊Dic3—91no—
508C4⋊Dic3—91no—
509C4⋊Dic3—181no—
510C4⋊Dic3D3211yescharacteristic
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—31no—
518Dic3⋊C4—31no—
519Dic3⋊C4—31no—
520Dic3⋊C4—31no—
521Dic3⋊C4—61no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—181no—
530Dic3⋊C4—181no—
531Dic3⋊C4D3211yescharacteristic
532Dic3⋊C4D3211yescharacteristic
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C4×Dic3—91no—
546C4×Dic3—181no—
547C4×Dic3—181no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—41no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C2×C3⋊D3—21no—
556C2×C3⋊D3—21no—
557C2×C3⋊D3—21no—
558C2×C3⋊D3—32no—
559C2×C3⋊D3—32no—
560C2×C3⋊D3—32no—
561C2×C3⋊D3—62no—
562C2×C3⋊D3—62no—
563C2×C3⋊D3—62no—
564C2×C3⋊D3—61no—
565C2×C3⋊D3—61no—
566C2×C3⋊D3—62no—
567C2×C3⋊D3—62no—
568C2×C3⋊D3—61no—
569C2×C3⋊D3—61no—
570C2×C3⋊D3—61no—
571C2×C3⋊D3—61no—
572C2×C3⋊D3—122no—
573C2×C3⋊D3—121no—
574C2×C3⋊D3—121no—
575C2×C3⋊D3—121no—
576C2×C3⋊D3—121no—
577C2×C3⋊D3—122no—
578C2×C3⋊D3—122no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—61no—
584C2×C3×D3—61no—
585C2×C3×D3—121no—
586C2×C3×D3—121no—
587C2×C3×D3—121no—
588C32×C4—21no—
589C32×C4—22no—
590C32×C4—21no—
591C32×C4—21no—
592C32×C4—32no—
593C32×C4—41no—
594C32×C4—41no—
595C32×C4—42no—
596C32×C4—61no—
597C32×C4—61no—
598C32×C4—61no—
599C32×C4—61no—
600C32×C4—61no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—21no—
605C3⋊Dic3—21no—
606C3⋊Dic3—61no—
607C3⋊Dic3—62no—
608C3⋊Dic3—61no—
609C3⋊Dic3—61no—
610C3⋊Dic3—121no—
611C3⋊Dic3—121no—
612C3⋊Dic3—122no—
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—21no—
622C3×Dic3—21no—
623C3×Dic3—22no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—41no—
627C3×Dic3—41no—
628C3×Dic3—41no—
629C3×Dic3—62no—
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—61no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642C3×Dic3—121no—
643C3×Dic3—121no—
644C3×Dic3#23712yes—
645C3×Dic3#23912yes—
646#126—271no—
647#126—271no—
648#125—91no—
649#125—91no—
650#125—271no—
651#123—271no—
652#123—271no—
653C22⋊Q8—91no—
654C22⋊Q8—271no—
655C4×Q8—271no—
656C4×D4—271no—
657#117—271no—
658#117—271no—
659#117—271no—
660C2×C4⋊C4—271no—
661C33#55211yescharacteristic, complemented, Sylow
662C23×C3—91no—
663C22×D3—31no—
664C22×D3—31no—
665C22×D3—61no—
666C22×D3—91no—
667C22×D3—91no—
668C22×D3—91no—
669C22×D3—181no—
670C22×D3—181no—
671C22×D3—181no—
672C22×D3—361no—
673C3×Q8—182no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
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—31no—
686C2×C3×C4—31no—
687C2×C3×C4—31no—
688C2×C3×C4—31no—
689C2×C3×C4—41no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—91no—
699C2×C3×C4—91no—
700C2×C3×C4—91no—
701C2×C3×C4—182no—
702C2×C3×C4C2×D3211yescharacteristic
703C2×C3×C4C2×D3211yescharacteristic
704C2×C3×C4C2×D3211yescharacteristic
705#67—182no—
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—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—91no—
722C2×Dic3—91no—
723C2×Dic3—91no—
724C2×Dic3—181no—
725C2×Dic3—181no—
726C2×Dic3—181no—
727C2×Dic3—361no—
728C2×Dic3C2×D3211yescharacteristic
729C2×Dic3C2×D3211yescharacteristic
730C2×Dic3C2×D3211yescharacteristic
731C2×Dic3C2×D3211yescharacteristic
732C2×Dic3C2×D3211yescharacteristic
733C2×Dic3C2×D3211yescharacteristic
734D12—182no—
735D12—182no—
736D12—362no—
737C4×D3—62no—
738C4×D3—62no—
739C4×D3—182no—
740C4×D3—182no—
741C4×D3—182no—
742C4×D3—182no—
743C4×D3—182no—
744C4×D3—184no—
745C4×D3—182no—
746C4×D3—182no—
747C4×D3—182no—
748C4×D3—184no—
749C4×D3—182no—
750C4×D3—362no—
751C4×D3—362no—
752C4×D3—362no—
753C4×D3—364no—
754Dic6—62no—
755Dic6—62no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—21no—
760C2×C32—21no—
761C2×C32—21no—
762C2×C32—21no—
763C2×C32—21no—
764C2×C32—21no—
765C2×C32—41no—
766C2×C32—41no—
767C2×C32—41no—
768C2×C32C2×#23711yescharacteristic
769C2×C32C2×#23911yescharacteristic
770C2×C32#100711yescharacteristic
771C2×C32#100711yescharacteristic
772C2×C32D3×#4111yescharacteristic
773C2×C32D3×#4111yescharacteristic
774C2×C32D3×#4111yescharacteristic
775C2×C32D3×#4111yescharacteristic
776C2×C32#101011yescharacteristic
777C3⋊D3—41no—
778C3⋊D3—62no—
779C3⋊D3—64no—
780C3⋊D3—62no—
781C3⋊D3—62no—
782C3⋊D3—122no—
783C3⋊D3—122no—
784C3⋊D3—124no—
785C3×D3—121no—
786C3×D3—121no—
787C3×D3—241no—
788C2×Q8—91no—
789C2×D4—271no—
790C22×C4—91no—
791C22×C4—271no—
792C22×C4—271no—
793C22×C4—271no—
794C4⋊C4—31no—
795C4⋊C4—31no—
796C4⋊C4—31no—
797C4⋊C4—91no—
798C4⋊C4—91no—
799C4⋊C4—91no—
800C4⋊C4—91no—
801C4⋊C4—91no—
802C4⋊C4—91no—
803C4⋊C4—91no—
804C4⋊C4—91no—
805C4⋊C4—91no—
806C4⋊C4—271no—
807C4⋊C4—271no—
808C4⋊C4—271no—
809C4⋊C4—271no—
810C22⋊C4—91no—
811C22⋊C4—91no—
812C22⋊C4—271no—
813C22⋊C4—271no—
814C22⋊C4—271no—
815C22⋊C4—271no—
816C22⋊C4—271no—
817C22⋊C4—271no—
818C42—91no—
819C42—91no—
820C42—271no—
821C42—271no—
822C42—271no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—41no—
827C22×C3—181no—
828C22×C3—181no—
829C22×C3—181no—
830C22×C3C22×D3211yescharacteristic
831C22×C3C22×D3211yescharacteristic
832C22×C3C22×D3211yescharacteristic
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—92no—
840C2×D3—92no—
841C2×D3—92no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—182no—
846C2×D3—182no—
847C2×D3—182no—
848C2×D3—182no—
849C2×D3—182no—
850C2×D3—181no—
851C2×D3—181no—
852C2×D3—181no—
853C2×D3—181no—
854C2×D3—181no—
855C2×D3—181no—
856C2×D3—362no—
857C2×D3—361no—
858C2×D3—361no—
859C2×D3—361no—
860C2×D3—361no—
861C2×D3—362no—
862C2×D3—362no—
863C3×C4—22no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—21no—
867C3×C4—32no—
868C3×C4—32no—
869C3×C4—41no—
870C3×C4—41no—
871C3×C4—42no—
872C3×C4—62no—
873C3×C4—61no—
874C3×C4—61no—
875C3×C4—61no—
876C3×C4—61no—
877C3×C4—61no—
878C3×C4—61no—
879C3×C4—61no—
880C3×C4—61no—
881C3×C4—61no—
882C3×C4—61no—
883C3×C4—121no—
884C3×C4—121no—
885C3×C4—121no—
886C3×C4—121no—
887C3×C4—121no—
888C3×C4—181no—
889C3×C4—181no—
890C3×C4—181no—
891C3×C4—181no—
892C3×C4—181no—
893Dic3—21no—
894Dic3—21no—
895Dic3—21no—
896Dic3—21no—
897Dic3—21no—
898Dic3—62no—
899Dic3—61no—
900Dic3—61no—
901Dic3—61no—
902Dic3—61no—
903Dic3—61no—
904Dic3—61no—
905Dic3—61no—
906Dic3—61no—
907Dic3—61no—
908Dic3—61no—
909Dic3—121no—
910Dic3—121no—
911Dic3—121no—
912Dic3—121no—
913Dic3—182no—
914Dic3—181no—
915Dic3—181no—
916Dic3—181no—
917Dic3—361no—
918Dic3—361no—
919Dic3—362no—
920Dic3#379612yes—
921C32—21no—
922C32—21no—
923C32—21no—
924C32—41no—
925C32#563911yescharacteristic, complemented
926C32#569311yescharacteristic, complemented
927C32#569411yescharacteristic, complemented
928C23—91no—
929C23—271no—
930Q8—182no—
931D4—542no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—31no—
935C2×C4—31no—
936C2×C4—31no—
937C2×C4—31no—
938C2×C4—91no—
939C2×C4—91no—
940C2×C4—91no—
941C2×C4—91no—
942C2×C4—91no—
943C2×C4—182no—
944C2×C4—271no—
945C2×C4—542no—
946C2×C4—542no—
947C2×C4—542no—
948C2×C4D3311yescharacteristic
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—41no—
959C2×C3—41no—
960C2×C3—41no—
961C2×C3—361no—
962C2×C3C2×#379611yescharacteristic
963C2×C3#6429711yescharacteristic
964C2×C3#6430611yescharacteristic
965C2×C3D3×#23711yescharacteristic
966C2×C3#6431211yescharacteristic
967C2×C3#6431211yescharacteristic
968C2×C3#6431511yescharacteristic
969C2×C3#6431611yescharacteristic
970C2×C3D3×#23911yescharacteristic
971D3—121no—
972D3—121no—
973D3—184no—
974D3—182no—
975D3—182no—
976D3—182no—
977D3—241no—
978D3—362no—
979D3—362no—
980D3—364no—
981C22—181no—
982C22—181no—
983C22—181no—
984C22—272no—
985C22—541no—
986C22—541no—
987C22C2×D3311yescharacteristic
988C4—21no—
989C4—32no—
990C4—61no—
991C4—61no—
992C4—61no—
993C4—61no—
994C4—61no—
995C4—181no—
996C4—181no—
997C4—181no—
998C4—181no—
999C4—181no—
1000C4—541no—
1001C3—21no—
1002C3—21no—
1003C3—21no—
1004C3—41no—
1005C3#1059433411yescharacteristic, complemented
1006C3#1059446911yescharacteristic, complemented
1007C3#1059457911yescharacteristic, complemented
1008C2—361no—
1009C2—542no—
1010C2D3×#379611yescharacteristic
1011C2#1172439711yescharacteristic
1012C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6292C22
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. #11723675C2semidirect
2. #11723470C2semidirect
4. #11723413C2semidirect
5. C3×#63895C2semidirect
6. C3×#63846C2semidirect
7. C3×#63845C2semidirect
8. #11723025C2semidirect
9. #11723015C2semidirect
11. #11722973C2semidirect
12. #11722940C2semidirect
14. #11722920C2semidirect
15. #11722915C2semidirect
67. #63895D3semidirect
93. #63846D3semidirect
94. #63845D3semidirect
661. C33#552semidirect
925. C32#5639semidirect
926. C32#5693semidirect
927. C32#5694semidirect
1005. C3#10594334semidirect
1006. C3#10594469semidirect
1007. C3#10594579semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117234702
#117234212
#117234132
C3×#638952
C3×#638462
C3×#638452
#117230252
#117230152
#117230002
#117229732
#117229402
#117229332
#117229202
#117229152
#105945793
#105944693
#105943343