Finite Group Databasebeta

← #13168320

Subgroups — #13168320

Order 1728.

1112 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723690C211yesmaximal, characteristic
2#11723497C211yesmaximal, characteristic, complemented
3#11723497C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63868C211yesmaximal, characteristic, complemented
6C3×#63845C211yesmaximal, characteristic, complemented
7C3×#63836C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723016C211yesmaximal, characteristic, complemented
10#11723014C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic
12#11722938C211yesmaximal, characteristic
13#11722922C211yesmaximal, characteristic, complemented
14#11722919C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10594478—31nomaximal
17#10594408—31nomaximal
18#10593919—31nomaximal
19C2×#6308C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×Dic3×C3⋊D3C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25C3×#3752C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C32×Dic3⋊C4C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31#88815C2211yescharacteristic
32#88814C2211yescharacteristic
33#88807C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64105—31no—
56C4×#634—31no—
57C3×#898—31no—
58C3×#892—31no—
59C3×#890—31no—
60C3×#889—31no—
61C3×#876—31no—
62C3×#872—31no—
63#63905—31no—
64#63902—31no—
65#63900—31no—
66#63896—31no—
67#63896—31no—
68#63896—31no—
69#63896—31no—
70#63896—61no—
71#63896—61no—
72#63891—31no—
73#63890—31no—
74#63881—31no—
75#63881—31no—
76#63878—31no—
77#63877—31no—
78#63877—31no—
79#63877—31no—
80D3×Dic3⋊C4—31no—
81D3×Dic3⋊C4—31no—
82#63874—31no—
83#63870—31no—
84#63868D311yescharacteristic, complemented
85#63867—31no—
86#63867—31no—
87#63862—31no—
88#63858—31no—
89#63854—31no—
90#63854—31no—
91#63850—31no—
92#63848—31no—
93#63847—31no—
94#63847—31no—
95#63847—31no—
96#63845D311yescharacteristic, complemented
97#63844—31no—
98#63844—31no—
99#63844—61no—
100#63836—31no—
101#63836D311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107#6308—22no—
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#6295—22no—
119#6294—22no—
120Dic3×C3⋊D3—22no—
121Dic3×C3⋊D3—22no—
122C3×#624—22no—
123#5708—91no—
124#5693—91no—
125#5531—91no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×#634—31no—
129C2×#634—31no—
130C2×#634—31no—
131C2×#634—61no—
132C2×#634—61no—
133C2×#634—61no—
134C2×#634—121no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#624—31no—
141C2×#624C2×D311yescharacteristic
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—61no—
149C2×D3×Dic3—61no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C42—31no—
153#3752—31no—
154#3752—31no—
155#3752C2×D311yescharacteristic
156#3752C2×D311yescharacteristic
157C4⋊(C3⋊Dic3)C2×D311yescharacteristic
158#3750—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
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—31no—
171C3×(C2×D3)⋊C4—31no—
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)⋊C4—61no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—61no—
185C3×Dic3⋊C4—21no—
186C3×Dic3⋊C4—21no—
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⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×Dic3⋊C4C2×D311yescharacteristic
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×C4×Dic3—21no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3C2×D311yescharacteristic
205C3×C4×Dic3C2×D311yescharacteristic
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—61no—
216#3724—61no—
217#3724—61no—
218#3724—61no—
219#3724C2×D311yescharacteristic
220#3724C2×D311yescharacteristic
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233#3722—31no—
234#3722C2×D311yescharacteristic
235#3722C2×D311yescharacteristic
236#3722C2×D311yescharacteristic
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—61no—
244(C2×D3)⋊Dic3—61no—
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—21no—
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3#4112yes—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3⋊(C3⋊Dic3)#4112yes—
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—21no—
273C3×#126—91no—
274C3×#125—91no—
275C3×#117—91no—
276#929—91no—
277C2×Dic3⋊C4—91no—
278#898—31no—
279#898—91no—
280#898—91no—
281#896—91no—
282#896—91no—
283#896—91no—
284#896—91no—
285#896—181no—
286#896—181no—
287#894—91no—
288#894—91no—
289#893—91no—
290#892—31no—
291#892—91no—
292D3×C4⋊C4—91no—
293D3×C4⋊C4—91no—
294#890—31no—
295#889—31no—
296#889—91no—
297#889—91no—
298#889—91no—
299#889—91no—
300#889—91no—
301#887—91no—
302#886—91no—
303#883—91no—
304#883—91no—
305#67⋊C4—91no—
306#67⋊C4—91no—
307#879—91no—
308#878—91no—
309#878—91no—
310#877—91no—
311#877—91no—
312#876—31no—
313#872—31no—
314#872—91no—
315#872—91no—
316#872—91no—
317#870—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C4×Dic6—181no—
321C22×C3⋊D3C22×D311yescharacteristic
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—31no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—31no—
327C22×C3×D3—61no—
328C22×C3×D3—61no—
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—31no—
338C2×C32×C4—41no—
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C22×D311yescharacteristic
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
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—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—121no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C4×C3⋊D3—62no—
361C4×C3⋊D3—62no—
362#634—62no—
363#634—62no—
364#634—62no—
365#634—64no—
366#634—122no—
367#634—122no—
368#634—124no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
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×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
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C3×C4×D3—62no—
400C3×C4×D3—62no—
401#626—62no—
402#626—62no—
403#625—62no—
404#624—22no—
405#624—62no—
406D3×Dic3—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411D3×Dic3—62no—
412D3×Dic3—122no—
413D3×Dic3—122no—
414#552—271noSylow
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C2×C332−1+411yescharacteristic
418C3×C3⋊D3—22no—
419C3×C3⋊D3—41no—
420C22×C3×C4—91no—
421C2×#67—91no—
422C2×#67—91no—
423C22×Dic3—91no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426C2×D12—91no—
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—181no—
436C2×C4×D3—181no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—181no—
441C2×Dic6—181no—
442C2×Dic6—181no—
443C2×Dic6—361no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—61no—
449C3×C4⋊C4—61no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C22⋊C4—91no—
461C3×C22⋊C4—91no—
462C3×C42—31no—
463C3×C42—31no—
464C3×C42—61no—
465C3×C42—91no—
466C3×C42—91no—
467#217—91no—
468#217—91no—
469#217—91no—
470(C2×D3)⋊C4—31no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—31no—
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—31no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—31no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
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—181no—
489(C2×D3)⋊C4—181no—
490C4⋊Dic3—31no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—61no—
497C4⋊Dic3—91no—
498C4⋊Dic3—91no—
499C4⋊Dic3—91no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
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—181no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—181no—
531Dic3⋊C4—181no—
532Dic3⋊C4D3211yescharacteristic
533Dic3⋊C4D3211yescharacteristic
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—181no—
545C4×Dic3—181no—
546C4×Dic3D3211yescharacteristic
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—41no—
551C22×C32C23×D311yescharacteristic
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C2×C3⋊D3—21no—
555C2×C3⋊D3—21no—
556C2×C3⋊D3—21no—
557C2×C3⋊D3—21no—
558C2×C3⋊D3—21no—
559C2×C3⋊D3#23512yes—
560C2×C3×D3—32no—
561C2×C3×D3—32no—
562C2×C3×D3—62no—
563C2×C3×D3—61no—
564C2×C3×D3—61no—
565C2×C3×D3—61no—
566C2×C3×D3—61no—
567C2×C3×D3—62no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—61no—
571C2×C3×D3—61no—
572C2×C3×D3—61no—
573C2×C3×D3—61no—
574C2×C3×D3—121no—
575C2×C3×D3—121no—
576C2×C3×D3—121no—
577C2×C3×D3—121no—
578C32×C4—21no—
579C32×C4—22no—
580C32×C4—21no—
581C32×C4—21no—
582C32×C4—41no—
583C32×C4—41no—
584C32×C4—42no—
585C32×C4—61no—
586C32×C4—61no—
587C32×C4—61no—
588C32×C4—61no—
589C32×C4—61no—
590C32×C4—61no—
591C3⋊Dic3—21no—
592C3⋊Dic3—21no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3—32no—
596C3⋊Dic3—32no—
597C3⋊Dic3—32no—
598C3⋊Dic3—62no—
599C3⋊Dic3—62no—
600C3⋊Dic3—62no—
601C3⋊Dic3—61no—
602C3⋊Dic3—62no—
603C3⋊Dic3—61no—
604C3⋊Dic3—61no—
605C3⋊Dic3—122no—
606C3⋊Dic3—121no—
607C3⋊Dic3—121no—
608C3⋊Dic3—122no—
609C3×Dic3—22no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
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—41no—
623C3×Dic3—41no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—41no—
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—121no—
636C3×Dic3—121no—
637C3×Dic3—121no—
638C3×Dic3—121no—
639#126—91no—
640#126—271no—
641#125—91no—
642#125—271no—
643#125—271no—
644#123—271no—
645#123—271no—
646C22⋊Q8—271no—
647C22⋊Q8—271no—
648C4×Q8—271no—
649C4×D4—271no—
650#117—91no—
651#117—271no—
652#117—271no—
653C2×C4⋊C4—271no—
654C33#55211yescharacteristic, complemented, Sylow
655C23×C3—91no—
656C23×C3—91no—
657C22×D3—31no—
658C22×D3—31no—
659C22×D3—31no—
660C22×D3—31no—
661C22×D3—61no—
662C22×D3—61no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
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—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—41no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4—91no—
688C2×C3×C4—91no—
689C2×C3×C4—182no—
690C2×C3×C4C2×D3211yescharacteristic
691C2×C3×C4C2×D3211yescharacteristic
692C2×C3×C4C2×D3211yescharacteristic
693#67—182no—
694#67—182no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
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—182no—
720C2×Dic3—182no—
721C2×Dic3—182no—
722C2×Dic3—361no—
723C2×Dic3—361no—
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726C2×Dic3C2×D3211yescharacteristic
727C2×Dic3C2×D3211yescharacteristic
728C2×Dic3C2×D3211yescharacteristic
729C2×Dic3C2×D3211yescharacteristic
730D12—182no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—182no—
734C4×D3—182no—
735C4×D3—182no—
736C4×D3—182no—
737C4×D3—182no—
738C4×D3—182no—
739C4×D3—362no—
740C4×D3—362no—
741Dic6—182no—
742Dic6—182no—
743Dic6—182no—
744Dic6—184no—
745Dic6—362no—
746Dic6—362no—
747Dic6—364no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32C2×#23511yescharacteristic
761C2×C32#100711yescharacteristic
762C2×C32D3×#4111yescharacteristic
763C2×C32D3×#4111yescharacteristic
764C2×C32D3×#4111yescharacteristic
765C2×C32D3×#4111yescharacteristic
766C2×C32D3×#4111yescharacteristic
767C2×C32#101011yescharacteristic
768C2×C32#101011yescharacteristic
769C3⋊D3—22no—
770C3⋊D3—41no—
771C3×D3—62no—
772C3×D3—62no—
773C3×D3—122no—
774C3×D3—122no—
775C3×D3—121no—
776C3×D3—121no—
777C2×Q8—271no—
778C2×D4—271no—
779C22×C4—91no—
780C22×C4—271no—
781C22×C4—271no—
782C22×C4—271no—
783C4⋊C4—31no—
784C4⋊C4—31no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—91no—
792C4⋊C4—271no—
793C4⋊C4—271no—
794C4⋊C4—271no—
795C4⋊C4—271no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C4⋊C4—271no—
799C22⋊C4—91no—
800C22⋊C4—91no—
801C22⋊C4—91no—
802C22⋊C4—91no—
803C22⋊C4—91no—
804C22⋊C4—271no—
805C22⋊C4—271no—
806C22⋊C4—271no—
807C42—31no—
808C42—91no—
809C42—91no—
810C42—271no—
811C42—271no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—41no—
816C22×C3—92no—
817C22×C3—181no—
818C22×C3—181no—
819C22×C3—181no—
820C22×C3—181no—
821C22×C3—181no—
822C22×C3C22×D3211yescharacteristic
823C22×C3C22×D3211yescharacteristic
824C22×C3C22×D3211yescharacteristic
825C2×D3—32no—
826C2×D3—32no—
827C2×D3—62no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—62no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C3×C4—22no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—41no—
848C3×C4—41no—
849C3×C4—42no—
850C3×C4—62no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—61no—
860C3×C4—61no—
861C3×C4—61no—
862C3×C4—61no—
863C3×C4—121no—
864C3×C4—121no—
865C3×C4—121no—
866C3×C4—121no—
867C3×C4—121no—
868C3×C4—181no—
869C3×C4—181no—
870C3×C4—181no—
871C3×C4—181no—
872Dic3—21no—
873Dic3—21no—
874Dic3—21no—
875Dic3—21no—
876Dic3—21no—
877Dic3—21no—
878Dic3—61no—
879Dic3—61no—
880Dic3—61no—
881Dic3—61no—
882Dic3—61no—
883Dic3—61no—
884Dic3—61no—
885Dic3—61no—
886Dic3—92no—
887Dic3—92no—
888Dic3—92no—
889Dic3—121no—
890Dic3—121no—
891Dic3—121no—
892Dic3—121no—
893Dic3—182no—
894Dic3—182no—
895Dic3—182no—
896Dic3—182no—
897Dic3—181no—
898Dic3—181no—
899Dic3—181no—
900Dic3—362no—
901Dic3—361no—
902Dic3—361no—
903Dic3—362no—
904C32—21no—
905C32—21no—
906C32—21no—
907C32—41no—
908C32#553111yescharacteristic, complemented
909C32#569311yescharacteristic, complemented
910C32#570811yescharacteristic, complemented
911C23—91no—
912C23—91no—
913Q8—542no—
914D4—542no—
915C2×C4—31no—
916C2×C4—31no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—91no—
922C2×C4—91no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—182no—
926C2×C4—271no—
927C2×C4—271no—
928C2×C4—542no—
929C2×C4—542no—
930C2×C4—542no—
931C2×C4D3311yescharacteristic
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—41no—
942C2×C3—41no—
943C2×C3—41no—
944C2×C3—182no—
945C2×C3—361no—
946C2×C3#6429711yescharacteristic
947C2×C3#6429811yescharacteristic
948C2×C3D3×#23511yescharacteristic
949C2×C3D3×#23511yescharacteristic
950C2×C3#6430611yescharacteristic
951C2×C3#6431211yescharacteristic
952C2×C3#6431211yescharacteristic
953C2×C3#6431511yescharacteristic
954C2×C3#6431911yescharacteristic
955D3—62no—
956D3—62no—
957D3—122no—
958D3—122no—
959D3—121no—
960D3—121no—
961C22—92no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22C2×D3311yescharacteristic
968C4—21no—
969C4—61no—
970C4—61no—
971C4—61no—
972C4—61no—
973C4—61no—
974C4—61no—
975C4—181no—
976C4—181no—
977C4—181no—
978C4—181no—
979C4—272no—
980C4—541no—
981C3—21no—
982C3—21no—
983C3—21no—
984C3—41no—
985C3#1059391911yescharacteristic, complemented
986C3#1059440811yescharacteristic, complemented
987C3#1059447811yescharacteristic, complemented
988C2—182no—
989C2—361no—
990C2#1172438911yescharacteristic
991C2#1172439611yescharacteristic
992C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6295C22
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
2. #11723497C2semidirect
3. #11723497C2semidirect
4. #11723399C2semidirect
5. C3×#63868C2semidirect
6. C3×#63845C2semidirect
7. C3×#63836C2semidirect
8. #11723025C2semidirect
9. #11723016C2semidirect
10. #11723014C2semidirect
13. #11722922C2semidirect
14. #11722919C2semidirect
15. #11722911C2semidirect
84. #63868D3semidirect
96. #63845D3semidirect
101. #63836D3semidirect
654. C33#552semidirect
908. C32#5531semidirect
909. C32#5693semidirect
910. C32#5708semidirect
985. C3#10593919semidirect
986. C3#10594408semidirect
987. C3#10594478semidirect

Maximal subgroups

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

subgroupindex
#117236902
#117234972
#117233992
C3×#638682
C3×#638452
C3×#638362
#117230252
#117230162
#117230142
#117229952
#117229382
#117229222
#117229192
#117229112
#105944783
#105944083
#105939193