Finite Group Databasebeta

← #13168455

Subgroups — #13168455

Order 1728.

1072 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723686C211yesmaximal, characteristic
2#11723488C211yesmaximal, characteristic
3#11723444C211yesmaximal, characteristic, complemented
4#11723405C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic
6C3×#63847C211yesmaximal, characteristic, complemented
7C3×#63837C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723023C211yesmaximal, characteristic, complemented
10#11722970C211yesmaximal, characteristic, complemented
11#11722970C211yesmaximal, characteristic, complemented
12#11722922C211yesmaximal, characteristic, complemented
13#11722919C211yesmaximal, characteristic, complemented
14#11722915C211yesmaximal, characteristic, complemented
15#11722908C211yesmaximal, characteristic, complemented
16#10594410—31nomaximal
17#10594349—31nomaximal
18#10593917—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×Dic3×C3⋊D3C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#624C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25#88857C2211yescharacteristic
26C3×#3750C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31#88814C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64103—31no—
55#64098—31no—
56#64079—31no—
57C3×#893—31no—
58C3×#889—31no—
59C3×#889—31no—
60C3×#887—31no—
61C3×C4×D12—31no—
62C3×C4×Dic6—31no—
63#63897—31no—
64#63894D311yescharacteristic
65D3×C4⋊Dic3—31no—
66D3×C4⋊Dic3—31no—
67#63888—31no—
68#63888—31no—
69#63884—31no—
70#63884—31no—
71#63884—31no—
72#63884—31no—
73#63884—61no—
74#63883—31no—
75#63878—31no—
76#63877—31no—
77#63877—31no—
78#63877—31no—
79#63874—31no—
80#63868—31no—
81#63868—31no—
82#63867—31no—
83#63867—31no—
84#63867—61no—
85#63861—31no—
86#63859—31no—
87#63859—31no—
88#63858—31no—
89#63856—31no—
90#63856—31no—
91#63855—31no—
92#63851—31no—
93#63851—31no—
94#63847—31no—
95#63847—31no—
96#63847—61no—
97#63847D311yescharacteristic, complemented
98#63841—31no—
99#63837D311yescharacteristic, complemented
100#63836—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊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
111C3×C4⋊(C3⋊D3)—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6294—22no—
119Dic3×C3⋊D3—22no—
120C3×#627—22no—
121C3×#624—22no—
122C3×#624—22no—
123#5693—91no—
124#5581—91no—
125#5541—91no—
126C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
127C2×C4×C3⋊D3—31no—
128C2×C3×D12—31no—
129C2×C3×D12—31no—
130C2×C3×D12—61no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×#627C2×D311yescharacteristic
138C2×#624—31no—
139C2×#624C2×D311yescharacteristic
140C2×#624C2×D311yescharacteristic
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—61no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C42—31no—
149#3752—31no—
150#3752—31no—
151#3752—31no—
152C4⋊(C3⋊Dic3)—31no—
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155#3750—31no—
156#3750—31no—
157#3750—31no—
158#3750—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—61no—
163#3750—61no—
164#3750—61no—
165#3750—121no—
166#3750C2×D311yescharacteristic
167#3750C2×D311yescharacteristic
168C4×C3⋊Dic3—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×C4⋊Dic3—21no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3C2×D311yescharacteristic
177C3×C4⋊Dic3C2×D311yescharacteristic
178C3×Dic3⋊C4—21no—
179C3×Dic3⋊C4—31no—
180C3×Dic3⋊C4—31no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—61no—
190C3×Dic3⋊C4—61no—
191C3×Dic3⋊C4C2×D311yescharacteristic
192C3×Dic3⋊C4C2×D311yescharacteristic
193C3×C4×Dic3—21no—
194C3×C4×Dic3—31no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3C2×D311yescharacteristic
201C3×C4×Dic3C2×D311yescharacteristic
202#3724—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—61no—
209#3724—61no—
210#3724—61no—
211#3724C2×D311yescharacteristic
212#3724C2×D311yescharacteristic
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—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722C2×D311yescharacteristic
231#3722C2×D311yescharacteristic
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
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—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247Dic32—31no—
248Dic32—31no—
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×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3#4112yes—
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×C4×Q8—91no—
275C3×C4×D4—91no—
276#946—91no—
277#946—91no—
278#935—91no—
279#935—91no—
280#926—91no—
281C2×C4⋊Dic3—91no—
282#924—91no—
283#924—91no—
284#898—91no—
285#898—91no—
286#896—91no—
287#896—91no—
288#894—91no—
289#894—91no—
290#894—91no—
291#894—91no—
292#894—181no—
293#893—31no—
294#892—91no—
295#892—91no—
296D3×C4⋊C4—91no—
297D3×C4⋊C4—91no—
298#889—31no—
299#889—31no—
300#889—91no—
301#889—91no—
302#889—91no—
303#889—91no—
304#889—181no—
305#887—31no—
306#879—91no—
307#879—91no—
308#877—91no—
309#877—91no—
310#876—91no—
311#876—91no—
312C4×D12—31no—
313#872—91no—
314#872—91no—
315#872—91no—
316#872—91no—
317#870—91no—
318#870—91no—
319#870—181no—
320C4×Dic6—31no—
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)—22no—
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—21no—
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—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
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
392C3×D12—62no—
393C3×D12—62no—
394C3×D12—122no—
395C3×C4×D3—62no—
396C3×C4×D3—62no—
397C3×C4×D3—62no—
398C3×C4×D3—62no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401#627—22no—
402#624—22no—
403#624—22no—
404#624—62no—
405D3×Dic3—62no—
406D3×Dic3—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—122no—
410#552—271noSylow
411C2×C33C2×#4111yescharacteristic
412C2×C33C2×#4111yescharacteristic
413C2×C332−1+411yescharacteristic
414C3×C3⋊D3—22no—
415C3×C3⋊D3—41no—
416C2×C3×Q8—91no—
417C2×C3×D4—91no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C22×Dic3—91no—
421C22×Dic3—91no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—61no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
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—181no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—61no—
441C3×C4⋊C4—61no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C42—31no—
451C3×C42—31no—
452C3×C42—61no—
453C3×C42—91no—
454C3×C42—91no—
455C3×C42—91no—
456#217—91no—
457#217—91no—
458#217—91no—
459#217—91no—
460#217—91no—
461#217—91no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
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—181no—
479(C2×D3)⋊C4—181no—
480(C2×D3)⋊C4—181no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—91no—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—181no—
491C4⋊Dic3—181no—
492C4⋊Dic3—181no—
493C4⋊Dic3D3211yescharacteristic
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—61no—
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—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—181no—
524Dic3⋊C4—181no—
525Dic3⋊C4—181no—
526Dic3⋊C4—181no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—361no—
531Dic3⋊C4D3211yescharacteristic
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—181no—
542C4×Dic3D3211yescharacteristic
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—41no—
547C22×C32C23×D311yescharacteristic
548C22×C32C23×D311yescharacteristic
549C22×C32C23×D311yescharacteristic
550C2×C3⋊D3—21no—
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3#23512yes—
556C2×C3×D3—32no—
557C2×C3×D3—32no—
558C2×C3×D3—62no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
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—61no—
569C2×C3×D3—121no—
570C2×C3×D3—121no—
571C2×C3×D3—121no—
572C2×C3×D3—121no—
573C2×C3×D3—121no—
574C32×C4—21no—
575C32×C4—21no—
576C32×C4—21no—
577C32×C4—32no—
578C32×C4—41no—
579C32×C4—41no—
580C32×C4—41no—
581C32×C4—61no—
582C32×C4—61no—
583C32×C4—61no—
584C32×C4—61no—
585C32×C4—61no—
586C32×C4—81no—
587C3⋊Dic3—21no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—61no—
592C3⋊Dic3—62no—
593C3⋊Dic3—61no—
594C3⋊Dic3—61no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—61no—
598C3⋊Dic3—121no—
599C3⋊Dic3—121no—
600C3⋊Dic3—122no—
601C3⋊Dic3—121no—
602C3⋊Dic3—121no—
603C3⋊Dic3—121no—
604C3⋊Dic3—241no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—22no—
616C3×Dic3—41no—
617C3×Dic3—41no—
618C3×Dic3—41no—
619C3×Dic3—41no—
620C3×Dic3—41no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—121no—
630C3×Dic3—121no—
631C3×Dic3—121no—
632C3×Dic3—121no—
633C3×Dic3#23512yes—
634C3×Dic3#23712yes—
635#126—271no—
636#126—271no—
637#125—91no—
638#125—271no—
639#125—271no—
640#123—271no—
641#123—271no—
642C22⋊Q8—271no—
643C22⋊Q8—271no—
644C4×Q8—91no—
645C4×D4—91no—
646#117—271no—
647#117—271no—
648#117—271no—
649C2×C4⋊C4—271no—
650C33#55211yescharacteristic, complemented, Sylow
651C23×C3—91no—
652C23×C3—91no—
653C22×D3—31no—
654C22×D3—31no—
655C22×D3—31no—
656C22×D3—31no—
657C22×D3—61no—
658C22×D3—61no—
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—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—61no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4—182no—
688C2×C3×C4—182no—
689C2×C3×C4C2×D3211yescharacteristic
690C2×C3×C4C2×D3211yescharacteristic
691C2×C3×C4C2×D3211yescharacteristic
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—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—181no—
711C2×Dic3—181no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—182no—
717C2×Dic3—182no—
718C2×Dic3—361no—
719C2×Dic3—361no—
720C2×Dic3C2×D3211yescharacteristic
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726D12—62no—
727D12—62no—
728D12—122no—
729C4×D3—62no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—182no—
734C4×D3—182no—
735C4×D3—182no—
736C4×D3—182no—
737C4×D3—362no—
738Dic6—62no—
739Dic6—62no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32—41no—
752C2×C32C2×#23511yescharacteristic
753C2×C32C2×#23511yescharacteristic
754C2×C32C2×#23711yescharacteristic
755C2×C32#100711yescharacteristic
756C2×C32#100711yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C2×C32#101011yescharacteristic
761C3⋊D3—22no—
762C3⋊D3—41no—
763C3×D3—62no—
764C3×D3—62no—
765C3×D3—122no—
766C3×D3—121no—
767C3×D3—121no—
768C3×D3—241no—
769C2×Q8—91no—
770C2×D4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—271no—
774C22×C4—271no—
775C4⋊C4—31no—
776C4⋊C4—31no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C22⋊C4—91no—
792C22⋊C4—91no—
793C22⋊C4—271no—
794C22⋊C4—271no—
795C22⋊C4—271no—
796C22⋊C4—271no—
797C22⋊C4—271no—
798C22⋊C4—271no—
799C42—31no—
800C42—91no—
801C42—91no—
802C42—91no—
803C42—271no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—41no—
808C22×C3—92no—
809C22×C3—181no—
810C22×C3—181no—
811C22×C3—181no—
812C22×C3—181no—
813C22×C3—181no—
814C22×C3C22×D3211yescharacteristic
815C22×C3C22×D3211yescharacteristic
816C22×C3C22×D3211yescharacteristic
817C2×D3—32no—
818C2×D3—32no—
819C2×D3—62no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—61no—
823C2×D3—61no—
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—
833C2×D3—121no—
834C2×D3—121no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—32no—
839C3×C4—32no—
840C3×C4—41no—
841C3×C4—41no—
842C3×C4—41no—
843C3×C4—62no—
844C3×C4—61no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—81no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4—121no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863C3×C4—181no—
864Dic3—21no—
865Dic3—21no—
866Dic3—21no—
867Dic3—21no—
868Dic3—21no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—121no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3—182no—
882Dic3—181no—
883Dic3—181no—
884Dic3—181no—
885Dic3—181no—
886Dic3—181no—
887Dic3—181no—
888Dic3—361no—
889Dic3—361no—
890Dic3—361no—
891Dic3—361no—
892Dic3—361no—
893Dic3—362no—
894Dic3—721no—
895Dic3#379512yes—
896C32—21no—
897C32—21no—
898C32—21no—
899C32—41no—
900C32#554111yescharacteristic, complemented
901C32#558111yescharacteristic, complemented
902C32#569311yescharacteristic, complemented
903C23—91no—
904C23—91no—
905Q8—182no—
906D4—182no—
907C2×C4—31no—
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
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×C4—542no—
922C2×C4—542no—
923C2×C4D3311yescharacteristic
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—41no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—182no—
937C2×C3—361no—
938C2×C3C2×#379511yescharacteristic
939C2×C3#6429711yescharacteristic
940C2×C3D3×#23511yescharacteristic
941C2×C3D3×#23511yescharacteristic
942C2×C3D3×#23511yescharacteristic
943C2×C3D3×#23711yescharacteristic
944C2×C3#6431211yescharacteristic
945C2×C3#6431511yescharacteristic
946C2×C3#6431611yescharacteristic
947D3—62no—
948D3—62no—
949D3—122no—
950D3—121no—
951D3—121no—
952D3—241no—
953C22—92no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22C2×D3311yescharacteristic
960C4—21no—
961C4—32no—
962C4—61no—
963C4—61no—
964C4—61no—
965C4—61no—
966C4—61no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4—181no—
971C4—541no—
972C4—541no—
973C3—21no—
974C3—21no—
975C3—21no—
976C3—41no—
977C3#1059391711yescharacteristic, complemented
978C3#1059434911yescharacteristic, complemented
979C3#1059441011yescharacteristic, complemented
980C2—182no—
981C2—361no—
982C2D3×#379511yescharacteristic
983C2#1172439711yescharacteristic
984C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×C4⋊(C3⋊D3)C22
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
3. #11723444C2semidirect
4. #11723405C2semidirect
6. C3×#63847C2semidirect
7. C3×#63837C2semidirect
8. #11723024C2semidirect
9. #11723023C2semidirect
10. #11722970C2semidirect
11. #11722970C2semidirect
12. #11722922C2semidirect
13. #11722919C2semidirect
14. #11722915C2semidirect
15. #11722908C2semidirect
97. #63847D3semidirect
99. #63837D3semidirect
650. C33#552semidirect
900. C32#5541semidirect
901. C32#5581semidirect
902. C32#5693semidirect
977. C3#10593917semidirect
978. C3#10594349semidirect
979. C3#10594410semidirect

Maximal subgroups

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

subgroupindex
#117236862
#117234882
#117234442
#117234052
C3×#638942
C3×#638472
C3×#638372
#117230242
#117230232
#117229702
#117229222
#117229192
#117229152
#117229082
#105944103
#105943493
#105939173