Finite Group Databasebeta

← #13168663

Subgroups — #13168663

Order 1728.

1110 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#11723675C211yesmaximal, characteristic, complemented
2#11723536C211yesmaximal, characteristic, complemented
3#11723508C211yesmaximal, characteristic
4#11723391C211yesmaximal, characteristic, complemented
5C3×#63861C211yesmaximal, characteristic, complemented
6C3×#63858C211yesmaximal, characteristic, complemented
7C3×#63848C211yesmaximal, characteristic, complemented
8#11723009C211yesmaximal, characteristic
9#11723009C211yesmaximal, characteristic
10#11722983C211yesmaximal, characteristic, complemented
11#11722980C211yesmaximal, characteristic, complemented
12#11722943C211yesmaximal, characteristic, complemented
13#11722942C211yesmaximal, characteristic, complemented
14#11722919C211yesmaximal, characteristic, complemented
15#11722916C211yesmaximal, characteristic, complemented
16#10594480—31nomaximal
17#10594472—31nomaximal
18#10594250—31nomaximal
19C2×#6293C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×#6290C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88813C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×Dic3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×#3722C2211yescharacteristic
46C3×#3722C2211yescharacteristic
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64097—31no—
55#64096—31no—
56#64090—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#898—31no—
60C3×#898—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63982—31no—
64#63957—31no—
65#63953—31no—
66#63953—31no—
67#63919—31no—
68#63919—31no—
69#63919—61no—
70C4×#627—31no—
71#63915—31no—
72#63915—31no—
73#63913—31no—
74#63913—31no—
75#63902—31no—
76#63902—31no—
77#63902—61no—
78#63899—31no—
79#63899—31no—
80#63896—31no—
81#63896—31no—
82#63877—31no—
83#63877—31no—
84#63877—31no—
85#63877—31no—
86#63874—31no—
87#63865—31no—
88#63861—31no—
89#63861D311yescharacteristic, complemented
90#63858—31no—
91#63858D311yescharacteristic, complemented
92#63848—31no—
93#63848D311yescharacteristic, complemented
94#63844—31no—
95#63844—31no—
96#63838—31no—
97#63838—31no—
98#63838—31no—
99#63838—61no—
100#63837—31no—
101#63837—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—
118#6293—22no—
119#6293—22no—
120#6290—22no—
121Dic3×C3⋊D3—22no—
122D3×C3⋊Dic3—22no—
123#5702—91no—
124#5702—91no—
125#5702—91no—
126C2×#638—31no—
127C22×C3⋊Dic3—31no—
128C2×C4×C3⋊D3—31no—
129C2×#634—31no—
130C2×#634—31no—
131C2×#634—31no—
132C2×#627—31no—
133C2×#627—31no—
134C2×#627—31no—
135C2×#627—31no—
136C2×#627—31no—
137C2×#627—31no—
138C2×#627—61no—
139C2×#627—61no—
140C2×#627—61no—
141C2×#625—31no—
142C2×#625—31no—
143C2×#625—61no—
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×C22⋊C4—31no—
153#3752C2×D311yescharacteristic
154C4⋊(C3⋊Dic3)C2×D311yescharacteristic
155#3750—31no—
156#3750—31no—
157#3750—31no—
158#3750—31no—
159#3750C2×D311yescharacteristic
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—61no—
166C4×C3⋊Dic3—61no—
167C4×C3⋊Dic3—61no—
168C4×C3⋊Dic3—121no—
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×(C2×D3)⋊C4—21no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—61no—
185C3×(C2×D3)⋊C4C2×D311yescharacteristic
186C3×(C2×D3)⋊C4C2×D311yescharacteristic
187C3×C4⋊Dic3—21no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—31no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—61no—
193C3×C4⋊Dic3C2×D311yescharacteristic
194C3×C4⋊Dic3C2×D311yescharacteristic
195C3×Dic3⋊C4—21no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—61no—
203C3×Dic3⋊C4C2×D311yescharacteristic
204C3×Dic3⋊C4C2×D311yescharacteristic
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—61no—
221#3724—61no—
222#3724—61no—
223#3724—61no—
224#3724C2×D311yescharacteristic
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229#3722—31no—
230#3722—31no—
231#3722C2×D311yescharacteristic
232#3722C2×D311yescharacteristic
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3C2×D311yescharacteristic
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240(C2×D3)⋊Dic3C2×D311yescharacteristic
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—61no—
249Dic32—61no—
250Dic32C2×D311yescharacteristic
251Dic32C2×D311yescharacteristic
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)#4112yes—
262C3⋊(C3⋊Dic3)#4112yes—
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—21no—
273C3×#126—91no—
274C3×#126—91no—
275C3×#126—91no—
276#898—31no—
277#898—31no—
278#898—31no—
279#898—31no—
280#898—91no—
281#898—91no—
282#896—91no—
283#896—91no—
284#896—91no—
285#888—91no—
286#888—91no—
287#888—91no—
288#888—181no—
289#887—91no—
290#887—91no—
291#887—91no—
292#887—91no—
293#887—91no—
294#887—91no—
295#887—181no—
296#885—91no—
297#885—91no—
298#885—91no—
299#885—91no—
300#885—91no—
301#885—91no—
302#67⋊C4—91no—
303#67⋊C4—91no—
304#67⋊C4—91no—
305#67⋊C4—181no—
306#879—31no—
307#879—31no—
308#879—91no—
309#878—91no—
310#878—91no—
311#878—91no—
312#877—91no—
313#877—91no—
314#877—91no—
315#872—91no—
316#872—91no—
317#872—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C4×Dic6—91no—
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
341#638—62no—
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—62no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3—121no—
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C4×C3⋊D3—62no—
363#634—62no—
364#634—62no—
365#634—62no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
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—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
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
395C2×C3×Dic3C22×D311yescharacteristic
396#627—62no—
397#627—62no—
398#627—62no—
399#627—62no—
400#627—62no—
401#627—62no—
402#627—64no—
403#627—122no—
404#627—122no—
405#625—62no—
406#625—62no—
407#625—64no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411D3×Dic3—62no—
412D3×Dic3—122no—
413D3×Dic3—122no—
414#556—271noSylow
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C2×C332−1+411yescharacteristic
418C3×C3⋊D3—41no—
419C32×D3—41no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—91no—
423C2×#67—181no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426C22×Dic3—91no—
427C22×Dic3—181no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—91no—
431C2×C4×D3—181no—
432C2×Dic6—91no—
433C2×Dic6—91no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
441C2×Dic6—181no—
442C2×Dic6—181no—
443C2×Dic6—181no—
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×C22⋊C4—31no—
456C3×C22⋊C4—31no—
457C3×C22⋊C4—61no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C22⋊C4—91no—
461C3×C22⋊C4—91no—
462C3×C22⋊C4—91no—
463C3×C22⋊C4—91no—
464C3×C22⋊C4—91no—
465C3×C42—91no—
466C3×C42—91no—
467C3×C42—91no—
468#217—31no—
469#217—31no—
470#217—31no—
471#217—31no—
472#217—91no—
473#217—91no—
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—31no—
481(C2×D3)⋊C4—31no—
482(C2×D3)⋊C4—31no—
483(C2×D3)⋊C4—31no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—91no—
488(C2×D3)⋊C4—91no—
489(C2×D3)⋊C4D3211yescharacteristic
490C4⋊Dic3—31no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—31no—
494C4⋊Dic3—61no—
495C4⋊Dic3—91no—
496C4⋊Dic3D3211yescharacteristic
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—61no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
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—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—181no—
519Dic3⋊C4—181no—
520Dic3⋊C4—181no—
521Dic3⋊C4—181no—
522Dic3⋊C4D3211yescharacteristic
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—31no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
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—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C4×Dic3—181no—
545C4×Dic3—181no—
546C4×Dic3—361no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—41no—
551C22×C32—61no—
552C22×C32—61no—
553C22×C32—61no—
554C22×C32C23×D311yescharacteristic
555C22×C32C23×D311yescharacteristic
556C22×C32C23×D311yescharacteristic
557C2×C3⋊D3—21no—
558C2×C3⋊D3—21no—
559C2×C3⋊D3—21no—
560C2×C3×D3—22no—
561C2×C3×D3—21no—
562C2×C3×D3—21no—
563C2×C3×D3—21no—
564C2×C3×D3—21no—
565C2×C3×D3—21no—
566C2×C3×D3—21no—
567C2×C3×D3—41no—
568C2×C3×D3—41no—
569C2×C3×D3—62no—
570C2×C3×D3—61no—
571C2×C3×D3—61no—
572C2×C3×D3—61no—
573C2×C3×D3—61no—
574C2×C3×D3—61no—
575C2×C3×D3—61no—
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—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3—21no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3—32no—
596C3⋊Dic3—32no—
597C3⋊Dic3—32no—
598C3⋊Dic3—32no—
599C3⋊Dic3—32no—
600C3⋊Dic3—32no—
601C3⋊Dic3—62no—
602C3⋊Dic3—62no—
603C3⋊Dic3—62no—
604C3⋊Dic3—62no—
605C3⋊Dic3—62no—
606C3⋊Dic3—62no—
607C3⋊Dic3—122no—
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—41no—
621C3×Dic3—41no—
622C3×Dic3—41no—
623C3×Dic3—41no—
624C3×Dic3—62no—
625C3×Dic3—61no—
626C3×Dic3—61no—
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—
639C4⋊Q8—271no—
640#126—91no—
641#126—91no—
642#126—91no—
643#126—271no—
644#124—271no—
645#124—271no—
646C22⋊Q8—271no—
647C22⋊Q8—271no—
648C4×Q8—271no—
649C4×Q8—271no—
650C4×Q8—271no—
651C4×D4—271no—
652#117—271no—
653#117—271no—
654C33#55611yescharacteristic, complemented, Sylow
655C23×C3—31no—
656C23×C3—31no—
657C23×C3—61no—
658C23×C3—91no—
659C22×D3—31no—
660C22×D3—31no—
661C22×D3—61no—
662C22×D3C2×D3211yescharacteristic
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—41no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4C2×D3211yescharacteristic
688C2×C3×C4C2×D3211yescharacteristic
689C2×C3×C4C2×D3211yescharacteristic
690#67—182no—
691#67—182no—
692#67—182no—
693#67—184no—
694C2×Dic3—31no—
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—31no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—91no—
713C2×Dic3—91no—
714C2×Dic3—91no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—181no—
720C2×Dic3—181no—
721C2×Dic3—182no—
722C2×Dic3—182no—
723C2×Dic3—182no—
724C2×Dic3—361no—
725C2×Dic3—361no—
726C2×Dic3—362no—
727C2×Dic3C2×D3211yescharacteristic
728C2×Dic3C2×D3211yescharacteristic
729C2×Dic3C2×D3211yescharacteristic
730C2×Dic3C2×D3211yescharacteristic
731C2×Dic3C2×D3211yescharacteristic
732C4×D3—182no—
733C4×D3—182no—
734C4×D3—182no—
735C4×D3—362no—
736Dic6—182no—
737Dic6—182no—
738Dic6—182no—
739Dic6—182no—
740Dic6—182no—
741Dic6—182no—
742Dic6—182no—
743Dic6—182no—
744Dic6—182no—
745Dic6—184no—
746Dic6—362no—
747Dic6—362no—
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×C32—121no—
761C2×C32D3×#4111yescharacteristic
762C2×C32D3×#4111yescharacteristic
763C2×C32D3×#4111yescharacteristic
764C2×C32D3×#4111yescharacteristic
765C2×C32D3×#4111yescharacteristic
766C2×C32D3×#4111yescharacteristic
767C2×C32#101011yescharacteristic
768C2×C32#101011yescharacteristic
769C2×C32#101011yescharacteristic
770C3⋊D3—41no—
771C3×D3—42no—
772C3×D3—41no—
773C3×D3—41no—
774C3×D3—122no—
775C3×D3—121no—
776C3×D3—121no—
777C2×Q8—271no—
778C2×Q8—271no—
779C2×Q8—271no—
780C2×D4—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—271no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C4⋊C4—271no—
794C4⋊C4—271no—
795C22⋊C4—31no—
796C22⋊C4—91no—
797C22⋊C4—91no—
798C22⋊C4—91no—
799C22⋊C4—91no—
800C22⋊C4—91no—
801C22⋊C4—91no—
802C22⋊C4—91no—
803C22⋊C4—271no—
804C22⋊C4—271no—
805C42—91no—
806C42—91no—
807C42—91no—
808C42—271no—
809C42—271no—
810C42—271no—
811C42—271no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—41no—
816C22×C3—62no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—181no—
826C22×C3—181no—
827C22×C3—181no—
828C22×C3C22×D3211yescharacteristic
829C22×C3C22×D3211yescharacteristic
830C22×C3C22×D3211yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—62no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—61no—
840C2×D3—61no—
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—121no—
862C3×C4—121no—
863C3×C4—121no—
864C3×C4—121no—
865C3×C4—181no—
866C3×C4—181no—
867C3×C4—181no—
868C3×C4—181no—
869C3×C4—181no—
870Dic3—21no—
871Dic3—21no—
872Dic3—21no—
873Dic3—21no—
874Dic3—21no—
875Dic3—62no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—61no—
880Dic3—61no—
881Dic3—61no—
882Dic3—61no—
883Dic3—61no—
884Dic3—61no—
885Dic3—61no—
886Dic3—92no—
887Dic3—92no—
888Dic3—92no—
889Dic3—92no—
890Dic3—92no—
891Dic3—92no—
892Dic3—121no—
893Dic3—121no—
894Dic3—121no—
895Dic3—121no—
896Dic3—182no—
897Dic3—182no—
898Dic3—182no—
899Dic3—182no—
900Dic3—182no—
901Dic3—182no—
902Dic3—362no—
903Dic3—362no—
904C32—21no—
905C32—21no—
906C32—21no—
907C32—41no—
908C32#570211yescharacteristic, complemented
909C32#570211yescharacteristic, complemented
910C32#570211yescharacteristic, complemented
911C23—31no—
912C23—91no—
913Q8—542no—
914Q8—542no—
915Q8—542no—
916D4—542no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—91no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—91no—
926C2×C4—91no—
927C2×C4—271no—
928C2×C4—271no—
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—122no—
945C2×C3—121no—
946C2×C3—121no—
947C2×C3—361no—
948C2×C3#6429811yescharacteristic
949C2×C3#6430611yescharacteristic
950C2×C3#6430611yescharacteristic
951C2×C3#6430911yescharacteristic
952C2×C3#6430911yescharacteristic
953C2×C3#6431211yescharacteristic
954C2×C3#6431211yescharacteristic
955C2×C3#6431911yescharacteristic
956C2×C3#6431911yescharacteristic
957D3—41no—
958D3—122no—
959D3—121no—
960D3—121no—
961C22—61no—
962C22—61no—
963C22—61no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22C2×D3311yescharacteristic
968C4—21no—
969C4—61no—
970C4—61no—
971C4—61no—
972C4—61no—
973C4—61no—
974C4—181no—
975C4—181no—
976C4—181no—
977C4—181no—
978C4—181no—
979C4—272no—
980C4—272no—
981C3—21no—
982C3—21no—
983C3—21no—
984C3—41no—
985C3#1059425011yescharacteristic, complemented
986C3#1059447211yescharacteristic, complemented
987C3#1059448011yescharacteristic, complemented
988C2—121no—
989C2—361no—
990C2#1172437611yescharacteristic
991C2#1172437611yescharacteristic
992C2#1172442711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6290C22
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. #11723536C2semidirect
4. #11723391C2semidirect
5. C3×#63861C2semidirect
6. C3×#63858C2semidirect
7. C3×#63848C2semidirect
10. #11722983C2semidirect
11. #11722980C2semidirect
12. #11722943C2semidirect
13. #11722942C2semidirect
14. #11722919C2semidirect
15. #11722916C2semidirect
89. #63861D3semidirect
91. #63858D3semidirect
93. #63848D3semidirect
654. C33#556semidirect
908. C32#5702semidirect
909. C32#5702semidirect
910. C32#5702semidirect
985. C3#10594250semidirect
986. C3#10594472semidirect
987. C3#10594480semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117235362
#117235082
#117233912
C3×#638612
C3×#638582
C3×#638482
#117230092
#117229832
#117229802
#117229432
#117229422
#117229192
#117229162
#105944803
#105944723
#105942503