Finite Group Databasebeta

← #13168297

Subgroups — #13168297

Order 1728.

1226 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723503C211yesmaximal, characteristic, complemented
3#11723462C211yesmaximal, characteristic
4#11723442C211yesmaximal, characteristic, complemented
5C3×#63899C211yesmaximal, characteristic, complemented
6C3×#63893C211yesmaximal, characteristic, complemented
7C3×#63847C211yesmaximal, characteristic, complemented
8#11723032C211yesmaximal, characteristic, complemented
9#11722980C211yesmaximal, characteristic, complemented
10#11722977C211yesmaximal, characteristic, complemented
11#11722973C211yesmaximal, characteristic, complemented
12#11722943C211yesmaximal, characteristic, complemented
13#11722935C211yesmaximal, characteristic
14#11722932C211yesmaximal, characteristic
15D3×#3724C211yesmaximal, characteristic, complemented
16#10594395—31nomaximal
17#10594394—31nomaximal
18#10594168—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35#88815C2211yescharacteristic
36#88815C2211yescharacteristic
37#88815C2211yescharacteristic
38#88813C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41#88806C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55C4⋊C4×C3⋊D3—31no—
56#64090—31no—
57C3×#897—31no—
58C3×#896—31no—
59C3×#889—31no—
60C3×#889—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63982—31no—
64C2×#3724—31no—
65#63952—31no—
66#63952—31no—
67#63904—31no—
68C4×#626—31no—
69#63900—31no—
70#63900—31no—
71#63900—61no—
72#63899—31no—
73#63899D311yescharacteristic, complemented
74#63896—31no—
75#63895—31no—
76#63893D311yescharacteristic, complemented
77#63888—31no—
78#63888—31no—
79#63888—31no—
80#63881—31no—
81#63881—31no—
82#63881—31no—
83#63881—61no—
84#63880—31no—
85D3×Dic3⋊C4—31no—
86D3×Dic3⋊C4—31no—
87#63873—31no—
88#63871—31no—
89#63865—31no—
90#63865—31no—
91#63865—31no—
92#63865—61no—
93#63847—31no—
94#63847D311yescharacteristic, complemented
95#63846—31no—
96#63845—31no—
97#63844—31no—
98#63839—31no—
99#63839—31no—
100#63838—31no—
101#63837—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×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×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6293—22no—
119#6291Q814yescomplemented
120#6289—41no—
121#6289—41no—
122D3×C3⋊Dic3—22no—
123C3×#627—41no—
124C3×#627—41no—
125C3×D3×Dic3—41no—
126C3×D3×Dic3—41no—
127#5690—91no—
128#5636—91no—
129#5636—91no—
130C2×#638—31no—
131C22×C3⋊Dic3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—61no—
138C2×C4×C3⋊D3—61no—
139C2×C4×C3⋊D3—61no—
140C2×C4×C3⋊D3—121no—
141C2×#634—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—31no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×#627—31no—
151C2×#627—31no—
152C2×#627—61no—
153C2×#627C2×D311yescharacteristic
154C2×#627C2×D311yescharacteristic
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—61no—
158C2×#624—31no—
159C2×#624—31no—
160C2×#624—31no—
161C2×#624—31no—
162C2×#624—61no—
163C2×#624—61no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—61no—
167C2×D3×Dic3C2×D311yescharacteristic
168C2×D3×Dic3C2×D311yescharacteristic
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C22⋊C4—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175C4⋊(C3⋊Dic3)C2×D311yescharacteristic
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750C2×D311yescharacteristic
180#3750C2×D311yescharacteristic
181C4×C3⋊Dic3—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×(C2×D3)⋊C4—21no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4C2×D311yescharacteristic
188C3×(C2×D3)⋊C4C2×D311yescharacteristic
189C3×C4⋊Dic3—21no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—61no—
195C3×C4⋊Dic3C2×D311yescharacteristic
196C3×C4⋊Dic3C2×D311yescharacteristic
197C3×Dic3⋊C4—21no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4C2×D311yescharacteristic
213C3×Dic3⋊C4C2×D311yescharacteristic
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225#3724—61no—
226#3724—61no—
227#3724—61no—
228#3724C2×D311yescharacteristic
229#3724C2×D311yescharacteristic
230#3724C2×D311yescharacteristic
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—61no—
246#3722—61no—
247#3722—61no—
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32C2×D311yescharacteristic
257C22×C33C2411yescharacteristic
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C3⋊(C3⋊D3)C2×Q812yes—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3C2×Q812yes—
264C33×C4—21no—
265C3⋊(C3⋊Dic3)#4112yes—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3C2×Q812yes—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C3×#125—91no—
278C3×C22⋊Q8—91no—
279C3×C22⋊Q8—91no—
280#946—91no—
281#946—91no—
282#944—91no—
283#944—91no—
284C4×#67—91no—
285C4×#67—91no—
286C2×Dic3⋊C4—91no—
287C2×Dic3⋊C4—91no—
288#897—31no—
289#897—91no—
290#896—31no—
291#896—91no—
292#896—91no—
293#896—91no—
294#896—91no—
295#896—91no—
296#896—91no—
297#896—91no—
298#896—181no—
299#893—91no—
300#893—91no—
301D3×C4⋊C4—91no—
302D3×C4⋊C4—91no—
303D3×C4⋊C4—91no—
304D3×C4⋊C4—91no—
305D3×C4⋊C4—181no—
306#890—91no—
307#889—31no—
308#889—31no—
309#889—91no—
310#889—91no—
311#888—91no—
312#887—91no—
313#887—91no—
314#67⋊C4—91no—
315#67⋊C4—91no—
316#67⋊C4—91no—
317#67⋊C4—91no—
318#67⋊C4—181no—
319#878—31no—
320#878—31no—
321#878—91no—
322#878—91no—
323C4×D12—91no—
324C4×Dic6—91no—
325C23×C32—31no—
326C22×C3⋊D3—31no—
327C22×C3⋊D3—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—61no—
330C22×C3⋊D3—61no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—121no—
333C22×C3×D3—21no—
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C22×D311yescharacteristic
336C2×C32×C4—21no—
337C2×C32×C4—21no—
338C2×C32×C4—21no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—41no—
345C2×C32×C4C22×D311yescharacteristic
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348#638—34no—
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—61no—
355C2×C3⋊Dic3—62no—
356C2×C3⋊Dic3—121no—
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C4×C3⋊D3—62no—
364C4×C3⋊D3—62no—
365C4×C3⋊D3—62no—
366C4×C3⋊D3—64no—
367C4×C3⋊D3—122no—
368C4×C3⋊D3—122no—
369C4×C3⋊D3—124no—
370C4×C3⋊D3—121no—
371C4×C3⋊D3—121no—
372#634—62no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—121no—
397C2×C3×Dic3—121no—
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C3×C4×D3—121no—
409C3×C4×D3—121no—
410C3×Dic6—121no—
411C3×Dic6—121no—
412C3×Dic6—121no—
413C3×Dic6—121no—
414#627—41no—
415#627—41no—
416#627—62no—
417#627—62no—
418#627—122no—
419#626—34no—
420#626—34no—
421#626—64no—
422#624—121no—
423#624—121no—
424#624—121no—
425#624—121no—
426#624—122no—
427#624—122no—
428D3×Dic3—41no—
429D3×Dic3—41no—
430D3×Dic3—62no—
431D3×Dic3—62no—
432D3×Dic3—122no—
433#554—271noSylow
434C2×C33C22×Q811yescharacteristic
435C2×C33C2×#4111yescharacteristic
436C2×C33H(5,𝔽2)11yescharacteristic
437C3⋊(C3⋊D3)—22no—
438C32×D3—22no—
439C2×C3×Q8—91no—
440C2×C3×Q8—91no—
441C22×C3×C4—91no—
442C22×C3×C4—91no—
443C2×#67—91no—
444C2×#67—91no—
445C2×#67—181no—
446C22×Dic3—31no—
447C22×Dic3—31no—
448C22×Dic3—91no—
449C22×Dic3—91no—
450C22×Dic3—181no—
451C2×D12—91no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—181no—
465C2×C4×D3—181no—
466C2×C4×D3—181no—
467C2×C4×D3—181no—
468C2×C4×D3—181no—
469C2×C4×D3—361no—
470C2×Dic6—31no—
471C2×Dic6—31no—
472C2×Dic6—31no—
473C2×Dic6—31no—
474C2×Dic6—91no—
475C2×Dic6—91no—
476C2×Dic6—91no—
477C2×Dic6—181no—
478C3×C4⋊C4—31no—
479C3×C4⋊C4—31no—
480C3×C4⋊C4—31no—
481C3×C4⋊C4—31no—
482C3×C4⋊C4—61no—
483C3×C4⋊C4—61no—
484C3×C4⋊C4—91no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C4⋊C4—91no—
488C3×C4⋊C4—91no—
489C3×C4⋊C4—91no—
490C3×C4⋊C4—91no—
491C3×C4⋊C4—91no—
492C3×C22⋊C4—31no—
493C3×C22⋊C4—31no—
494C3×C22⋊C4—61no—
495C3×C22⋊C4—91no—
496C3×C22⋊C4—91no—
497C3×C42—91no—
498#217—31no—
499#217—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—181no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4D3211yescharacteristic
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—61no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3D3211yescharacteristic
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—61no—
537Dic3⋊C4—61no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—181no—
554Dic3⋊C4—181no—
555Dic3⋊C4—181no—
556Dic3⋊C4D3211yescharacteristic
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C4×Dic3—91no—
565C4×Dic3—181no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—32no—
570C22×C32—41no—
571C22×C32—61no—
572C22×C32—61no—
573C22×C32C23×D311yescharacteristic
574C22×C32C23×D311yescharacteristic
575C22×C32C23×D311yescharacteristic
576C2×C3⋊D3—32no—
577C2×C3⋊D3—32no—
578C2×C3⋊D3—32no—
579C2×C3⋊D3—62no—
580C2×C3⋊D3—62no—
581C2×C3⋊D3—62no—
582C2×C3⋊D3—61no—
583C2×C3⋊D3—61no—
584C2×C3⋊D3—62no—
585C2×C3⋊D3—62no—
586C2×C3⋊D3—61no—
587C2×C3⋊D3—61no—
588C2×C3⋊D3—61no—
589C2×C3⋊D3—61no—
590C2×C3⋊D3—122no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—121no—
594C2×C3⋊D3—121no—
595C2×C3⋊D3—122no—
596C2×C3⋊D3—122no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—22no—
602C2×C3×D3—41no—
603C2×C3×D3—41no—
604C2×C3×D3D3×Q812yes—
605C2×C3×D3D3×Q812yes—
606C32×C4—21no—
607C32×C4—22no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—41no—
611C32×C4—41no—
612C32×C4—42no—
613C32×C4—61no—
614C32×C4—61no—
615C32×C4—61no—
616C32×C4—61no—
617C32×C4—61no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—21no—
623C3⋊Dic3—32no—
624C3⋊Dic3—32no—
625C3⋊Dic3—32no—
626C3⋊Dic3—62no—
627C3⋊Dic3—62no—
628C3⋊Dic3—62no—
629C3⋊Dic3—122no—
630C3⋊Dic3D3×Q812yes—
631C3×Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—32no—
642C3×Dic3—32no—
643C3×Dic3—41no—
644C3×Dic3—41no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—62no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—121no—
660C3×Dic3—121no—
661C3×Dic3—121no—
662C3×Dic3—121no—
663C3×Dic3—121no—
664C4⋊Q8—271no—
665#125—91no—
666#125—271no—
667C22⋊Q8—91no—
668C22⋊Q8—91no—
669C22⋊Q8—271no—
670C22⋊Q8—271no—
671C22⋊Q8—271no—
672C22⋊Q8—271no—
673C4×Q8—271no—
674C4×D4—271no—
675C4×D4—271no—
676C4×D4—271no—
677C2×C4⋊C4—271no—
678C2×C4⋊C4—271no—
679C33#55411yescharacteristic, complemented, Sylow
680C23×C3—31no—
681C23×C3—31no—
682C23×C3—61no—
683C22×D3—91no—
684C22×D3—91no—
685C22×D3—91no—
686C22×D3—181no—
687C22×D3—181no—
688C22×D3—181no—
689C22×D3—361no—
690C22×D3C2×D3211yescharacteristic
691C3×Q8—361no—
692C3×Q8—361no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—41no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—91no—
715C2×C3×C4—91no—
716C2×C3×C4—91no—
717C2×C3×C4—91no—
718C2×C3×C4—361no—
719C2×C3×C4—361no—
720C2×C3×C4C2×D3211yescharacteristic
721C2×C3×C4C2×D3211yescharacteristic
722C2×C3×C4C2×D3211yescharacteristic
723#67—94no—
724#67—94no—
725#67—184no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—91no—
747C2×Dic3—121no—
748C2×Dic3—121no—
749C2×Dic3—181no—
750C2×Dic3—181no—
751C2×Dic3—181no—
752C2×Dic3—182no—
753C2×Dic3—182no—
754C2×Dic3—361no—
755C2×Dic3—362no—
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758C2×Dic3C2×D3211yescharacteristic
759C2×Dic3C2×D3211yescharacteristic
760C2×Dic3C2×D3211yescharacteristic
761D12—94no—
762C4×D3—121no—
763C4×D3—121no—
764C4×D3—182no—
765C4×D3—182no—
766C4×D3—182no—
767C4×D3—182no—
768C4×D3—184no—
769C4×D3—362no—
770C4×D3—362no—
771C4×D3—364no—
772C4×D3—361no—
773C4×D3—361no—
774C4×D3—361no—
775C4×D3—361no—
776C4×D3—361no—
777C4×D3—361no—
778C4×D3—362no—
779C4×D3—362no—
780Dic6—121no—
781Dic6—121no—
782Dic6—121no—
783Dic6—121no—
784Dic6—182no—
785Dic6—182no—
786Dic6—182no—
787Dic6—362no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—41no—
798C2×C32—41no—
799C2×C32—41no—
800C2×C32—62no—
801C2×C32#100411yescharacteristic
802C2×C32#100411yescharacteristic
803C2×C32C2×D3×Q811yescharacteristic
804C2×C32C2×D3×Q811yescharacteristic
805C2×C32C2×D3×Q811yescharacteristic
806C2×C32D3×#4111yescharacteristic
807C2×C32D3×#4111yescharacteristic
808C2×C32D3×#4111yescharacteristic
809C2×C32#100911yescharacteristic
810C3⋊D3—62no—
811C3⋊D3—64no—
812C3⋊D3—62no—
813C3⋊D3—62no—
814C3⋊D3—122no—
815C3⋊D3—122no—
816C3⋊D3—124no—
817C3×D3—22no—
818C3×D3—22no—
819C3×D3—42no—
820C2×Q8—91no—
821C2×Q8—91no—
822C2×Q8—271no—
823C2×D4—271no—
824C22×C4—91no—
825C22×C4—91no—
826C22×C4—271no—
827C22×C4—271no—
828C22×C4—271no—
829C22×C4—271no—
830C4⋊C4—31no—
831C4⋊C4—31no—
832C4⋊C4—91no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C4⋊C4—271no—
846C22⋊C4—31no—
847C22⋊C4—91no—
848C22⋊C4—91no—
849C22⋊C4—271no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C42—91no—
853C42—271no—
854C42—271no—
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—32no—
859C22×C3—32no—
860C22×C3—41no—
861C22×C3—62no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—61no—
865C22×C3—61no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3C22×D3211yescharacteristic
869C22×C3C22×D3211yescharacteristic
870C22×C3C22×D3211yescharacteristic
871C2×D3—21no—
872C2×D3—21no—
873C2×D3—92no—
874C2×D3—92no—
875C2×D3—92no—
876C2×D3—182no—
877C2×D3—182no—
878C2×D3—182no—
879C2×D3—182no—
880C2×D3—182no—
881C2×D3—181no—
882C2×D3—181no—
883C2×D3—181no—
884C2×D3—181no—
885C2×D3—181no—
886C2×D3—181no—
887C2×D3—362no—
888C2×D3—361no—
889C2×D3—361no—
890C2×D3—361no—
891C2×D3—361no—
892C2×D3—362no—
893C2×D3—362no—
894C2×D3#379712yes—
895C3×C4—22no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—42no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—61no—
908C3×C4—61no—
909C3×C4—61no—
910C3×C4—61no—
911C3×C4—61no—
912C3×C4—92no—
913C3×C4—121no—
914C3×C4—121no—
915C3×C4—121no—
916C3×C4—121no—
917C3×C4—121no—
918C3×C4—181no—
919C3×C4—181no—
920C3×C4—181no—
921C3×C4—181no—
922C3×C4—181no—
923Dic3—21no—
924Dic3—21no—
925Dic3—21no—
926Dic3—21no—
927Dic3—21no—
928Dic3—32no—
929Dic3—32no—
930Dic3—62no—
931Dic3—61no—
932Dic3—61no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—61no—
941Dic3—92no—
942Dic3—92no—
943Dic3—92no—
944Dic3—121no—
945Dic3—121no—
946Dic3—121no—
947Dic3—121no—
948Dic3—121no—
949Dic3—182no—
950Dic3—182no—
951Dic3—182no—
952Dic3—362no—
953C32—21no—
954C32—21no—
955C32—21no—
956C32—41no—
957C32#563611yescharacteristic, complemented
958C32#563611yescharacteristic, complemented
959C32#569011yescharacteristic, complemented
960C23—31no—
961C23—271no—
962Q8—361no—
963Q8—361no—
964Q8—542no—
965D4—274no—
966C2×C4—31no—
967C2×C4—31no—
968C2×C4—31no—
969C2×C4—31no—
970C2×C4—31no—
971C2×C4—91no—
972C2×C4—91no—
973C2×C4—91no—
974C2×C4—91no—
975C2×C4—91no—
976C2×C4—91no—
977C2×C4—271no—
978C2×C4—361no—
979C2×C4—361no—
980C2×C4—542no—
981C2×C4—542no—
982C2×C4—1081no—
983C2×C4—1081no—
984C2×C4D3311yescharacteristic
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—41no—
995C2×C3—41no—
996C2×C3—41no—
997C2×C3—62no—
998C2×C3—62no—
999C2×C3—122no—
1000C2×C3C2×#379711yescharacteristic
1001C2×C3#6430611yescharacteristic
1002C2×C3#6430711yescharacteristic
1003C2×C3#6431211yescharacteristic
1004C2×C3#6431211yescharacteristic
1005C2×C3#6431311yescharacteristic
1006C2×C3#6431411yescharacteristic
1007C2×C3D32×Q811yescharacteristic
1008C2×C3D32×Q811yescharacteristic
1009D3—22no—
1010D3—184no—
1011D3—182no—
1012D3—182no—
1013D3—182no—
1014D3—362no—
1015D3—362no—
1016D3—364no—
1017C22—32no—
1018C22—61no—
1019C22—61no—
1020C22—272no—
1021C22—541no—
1022C22—541no—
1023C22C2×D3311yescharacteristic
1024C4—21no—
1025C4—61no—
1026C4—61no—
1027C4—61no—
1028C4—61no—
1029C4—61no—
1030C4—92no—
1031C4—181no—
1032C4—181no—
1033C4—181no—
1034C4—181no—
1035C4—181no—
1036C4—272no—
1037C3—21no—
1038C3—21no—
1039C3—21no—
1040C3—41no—
1041C3#1059416811yescharacteristic, complemented
1042C3#1059439411yescharacteristic, complemented
1043C3#1059439511yescharacteristic, complemented
1044C2—62no—
1045C2—542no—
1046C2D3×#379711yescharacteristic
1047C2#1172438111yescharacteristic
1048C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6291C22
hypercenterC2×C4D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723669C2semidirect
2. #11723503C2semidirect
4. #11723442C2semidirect
5. C3×#63899C2semidirect
6. C3×#63893C2semidirect
7. C3×#63847C2semidirect
8. #11723032C2semidirect
9. #11722980C2semidirect
10. #11722977C2semidirect
11. #11722973C2semidirect
12. #11722943C2semidirect
15. D3×#3724C2semidirect
73. #63899D3semidirect
76. #63893D3semidirect
94. #63847D3semidirect
119. #6291Q8semidirect
679. C33#554semidirect
957. C32#5636semidirect
958. C32#5636semidirect
959. C32#5690semidirect
1041. C3#10594168semidirect
1042. C3#10594394semidirect
1043. C3#10594395semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117235032
#117234622
#117234422
C3×#638992
C3×#638932
C3×#638472
#117230322
#117229802
#117229772
#117229732
#117229432
#117229352
#117229322
D3×#37242
#105943953
#105943943
#105941683