Finite Group Databasebeta

← #13178290

Subgroups — #13178290

Order 1728.

1298 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64094C211yesmaximal, characteristic, complemented
2C3×#64093C211yesmaximal, characteristic, complemented
3C3×#64090C211yesmaximal, characteristic, complemented
4#11723729C211yesmaximal, characteristic, complemented
5#11723725C211yesmaximal, characteristic, complemented
6#11723720C211yesmaximal, characteristic, complemented
7#11723717C211yesmaximal, characteristic, complemented
8#11723701C211yesmaximal, characteristic, complemented
9#11723700C211yesmaximal, characteristic, complemented
10#11723694C211yesmaximal, characteristic, complemented
11C4×#6295C211yesmaximal, characteristic, complemented
12#11723688C211yesmaximal, characteristic, complemented
13#11723677C211yesmaximal, characteristic, complemented
14#11723676C211yesmaximal, characteristic, complemented
15#11723676C211yesmaximal, characteristic, complemented
16#10594306—31nomaximal
17#10594298—31nomaximal
18#10594297—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×#634C2211yescharacteristic, complemented
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6294C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic, complemented
33C3×#3757C2211yescharacteristic, complemented
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3750C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88815C2211yescharacteristic, complemented
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#64094D311yescharacteristic, complemented
55#64093D311yescharacteristic, complemented
56#64090D311yescharacteristic, complemented
57C3×#885—31no—
58C3×#885—31no—
59C3×#885—61no—
60C3×#884—31no—
61C3×#884—31no—
62C3×#884—61no—
63C3×#67⋊C4—31no—
64C3×#67⋊C4—31no—
65C3×#67⋊C4—61no—
66#63983—31no—
67#63983—31no—
68#63983—31no—
69#63980—31no—
70#63978—31no—
71#63978—31no—
72#63971—31no—
73#63970—31no—
74#63966—31no—
75#63962—31no—
76#63961—31no—
77#63958—31no—
78#63923—31no—
79#63922—31no—
80#63922—31no—
81#63921—31no—
82D3×(C2×D3)⋊C4—31no—
83D3×(C2×D3)⋊C4—31no—
84#63905—31no—
85C4×#626—31no—
86C4×#626—31no—
87C4×#625—31no—
88#63896—31no—
89#63888—31no—
90#63887—31no—
91#63868—31no—
92#63868—31no—
93#63864—31no—
94#63863—31no—
95#63862—31no—
96#63862—31no—
97#63860—31no—
98#63859—31no—
99#63859—31no—
100#63853—31no—
101#63850—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C2×#1113—22no—
108C2×#1113—41no—
109C2×#1113—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C33×C4C2311yescharacteristic
112C3×#638—22no—
113C3×#638—41no—
114C3×#638—41no—
115C3×#638—41no—
116C2×C3×C3⋊Dic3—41no—
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C3×C4⋊(C3⋊D3)—41no—
126C3×C4×C3⋊D3—41no—
127C3×C4×C3⋊D3—41no—
128C3×#634—41no—
129#6295—22no—
130#6295—41no—
131#6294—41no—
132#5678—91no—
133#5613—91no—
134#5560—91no—
135C22×D32—31no—
136C22×D32—31no—
137C22×D32—31no—
138C2×#638C2×D311yescharacteristic
139C2×#638C2×D311yescharacteristic
140C2×#638C2×D311yescharacteristic
141C2×#638C2×D311yescharacteristic, complemented
142C22×C3⋊Dic3C2×D311yescharacteristic, complemented
143C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
144C2×C4×C3⋊D3C2×D311yescharacteristic
145C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
146C2×#634C2×D311yescharacteristic, complemented
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—61no—
156C2×C3×#67—61no—
157C2×C3×#67—61no—
158C2×C3×#67—61no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—61no—
162C2×C3×D12—31no—
163C2×C3×D12—31no—
164C2×C3×D12—61no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—61no—
170C2×C3×C4×D3—61no—
171C2×C3×Dic6—31no—
172C2×C3×Dic6—31no—
173C2×C3×Dic6—61no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#625—31no—
179C2×#625—31no—
180C2×#624—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C32×C22⋊C4—21no—
184C32×C22⋊C4—21no—
185C32×C22⋊C4—21no—
186C32×C22⋊C4—41no—
187C32×C22⋊C4C2×D311yescharacteristic, complemented
188C32×C22⋊C4C2×D311yescharacteristic, complemented
189C32×C22⋊C4C2×D311yescharacteristic, complemented
190#3757C2×D311yescharacteristic, complemented
191#3752C2×D311yescharacteristic
192#3752C2×D311yescharacteristic
193#3752C2×D311yescharacteristic
194#3752C2×D311yescharacteristic
195#3750C2×D311yescharacteristic, complemented
196#3750C2×D311yescharacteristic, complemented
197C4×C3⋊Dic3C2×D311yescharacteristic, complemented
198C4×C3⋊Dic3C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—61no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—61no—
211C3×(C2×D3)⋊C4—61no—
212C3×(C2×D3)⋊C4—61no—
213C3×(C2×D3)⋊C4—61no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—61no—
219C3×Dic3⋊C4—61no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—61no—
225C3×C4×Dic3—61no—
226#3724—31no—
227#3724—31no—
228#3724—31no—
229#3724—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3#4112yes—
278#1113—44no—
279C33×C4—21no—
280C33×C4—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×#124—91no—
290C3×#121—91no—
291C3×C4×D4—91no—
292#947—91no—
293#946—91no—
294#939—91no—
295#939—91no—
296#939—91no—
297#938—91no—
298#937—91no—
299#937—91no—
300#937—91no—
301#937—91no—
302#936—91no—
303#935—91no—
304#930—91no—
305#929—91no—
306#929—91no—
307C4×#67—91no—
308C4×#67—91no—
309C2×(C2×D3)⋊C4—91no—
310#898—91no—
311#898—91no—
312#896—91no—
313#894—91no—
314#886—91no—
315#885—31no—
316#885—31no—
317#885—61no—
318#884—31no—
319#884—31no—
320#884—61no—
321#884—91no—
322#883—91no—
323#882—91no—
324#882—91no—
325#67⋊C4—31no—
326#67⋊C4—31no—
327#67⋊C4—61no—
328D3×C22⋊C4—91no—
329D3×C22⋊C4—91no—
330#879—91no—
331#879—91no—
332#878—91no—
333#876—91no—
334#876—91no—
335#875—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—41no—
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—61no—
357C22×C3×D3—61no—
358C22×C3×D3—61no—
359C22×C3×D3—61no—
360C2×D32—62no—
361C2×D32—62no—
362C2×D32—62no—
363C2×D32—121no—
364C2×D32—121no—
365C2×D32—121no—
366C2×D32—121no—
367C2×D32—121no—
368C2×D32—121no—
369C2×C32×C4—21no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—21no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—41no—
376C2×C32×C4—41no—
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C22×D311yescharacteristic
380C2×C32×C4C22×D311yescharacteristic
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383#638—22no—
384#638—41no—
385#638—41no—
386#638—41no—
387C2×C3⋊Dic3—41no—
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
396C4⋊(C3⋊D3)—41no—
397C4×C3⋊D3—41no—
398C4×C3⋊D3—41no—
399#634—41no—
400C3×#67—62no—
401C3×#67—62no—
402C3×#67—64no—
403C3×#67—121no—
404C3×#67—121no—
405C3×#67—121no—
406C3×#67—121no—
407C3×#67—121no—
408C3×#67—121no—
409C3×#67—122no—
410C3×#67—122no—
411C3×#67—122no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—121no—
437C2×C3×Dic3—121no—
438C2×C3×Dic3—122no—
439C3×D12—121no—
440C3×D12—121no—
441C3×D12—122no—
442C3×C4×D3—121no—
443C3×C4×D3—121no—
444C3×C4×D3—121no—
445C3×C4×D3—121no—
446C3×C4×D3—122no—
447C3×C4×D3—122no—
448C3×Dic6—121no—
449C3×Dic6—121no—
450C3×Dic6—122no—
451#626—62no—
452#626—62no—
453#626—121no—
454#626—121no—
455#625—62no—
456#625—121no—
457#624—121no—
458D3×Dic3—121no—
459D3×Dic3—121no—
460#538—271noSylow
461C2×C33—41no—
462C2×C33C2×#4111yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C2×C33H(5,𝔽2)11yescharacteristic
465C3×C3⋊D3—22no—
466C3×C3⋊D3—41no—
467C3×C3⋊D3—41no—
468C3×C3⋊D3—41no—
469C23×D3—91no—
470C23×D3—91no—
471C23×D3—91no—
472C2×C3×Q8—91no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C2×C3×D4—91no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C22×C3×C4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—61no—
490C2×#67—61no—
491C2×#67—61no—
492C2×#67—61no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C22×Dic3—31no—
498C22×Dic3—31no—
499C22×Dic3—61no—
500C22×Dic3—91no—
501C2×D12—31no—
502C2×D12—31no—
503C2×D12—61no—
504C2×D12—91no—
505C2×D12—91no—
506C2×C4×D3—31no—
507C2×C4×D3—31no—
508C2×C4×D3—31no—
509C2×C4×D3—31no—
510C2×C4×D3—61no—
511C2×C4×D3—61no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×Dic6—31no—
515C2×Dic6—31no—
516C2×Dic6—61no—
517C3×C4⋊C4—91no—
518C3×C4⋊C4—91no—
519C3×C22⋊C4—21no—
520C3×C22⋊C4—21no—
521C3×C22⋊C4—21no—
522C3×C22⋊C4—41no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4D3211yescharacteristic, complemented
529C3×C22⋊C4D3211yescharacteristic, complemented
530C3×C22⋊C4D3211yescharacteristic, complemented
531C3×C42—91no—
532C3×C42—91no—
533#217—31no—
534#217—31no—
535#217—61no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—61no—
553(C2×D3)⋊C4—61no—
554(C2×D3)⋊C4—61no—
555(C2×D3)⋊C4—61no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572C4⋊Dic3—91no—
573C4⋊Dic3—91no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—61no—
581Dic3⋊C4—61no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590C4×Dic3—31no—
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—31no—
594C4×Dic3—61no—
595C4×Dic3—61no—
596C22×C32—21no—
597C22×C32—22no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—41no—
610C22×C32—41no—
611C22×C32—41no—
612C22×C32—42no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—81no—
620C22×C32—81no—
621C22×C32C23×D311yescharacteristic
622C22×C32C23×D311yescharacteristic
623C22×C32C23×D311yescharacteristic
624C2×C3⋊D3—21no—
625C2×C3⋊D3—21no—
626C2×C3⋊D3—21no—
627C2×C3⋊D3—21no—
628C2×C3⋊D3—21no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3#23512yes—
636C2×C3×D3—32no—
637C2×C3×D3—32no—
638C2×C3×D3—62no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—62no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—121no—
663C2×C3×D3—121no—
664C2×C3×D3—121no—
665C2×C3×D3—121no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672D32—124no—
673D32—124no—
674D32—124no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—21no—
679C32×C4—21no—
680C32×C4—21no—
681C32×C4—41no—
682C32×C4—41no—
683C32×C4—41no—
684C32×C4—41no—
685C32×C4—41no—
686C32×C4—41no—
687C32×C4—81no—
688C32×C4—81no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3⋊Dic3—21no—
692C3⋊Dic3—21no—
693C3⋊Dic3—21no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3×Dic3—62no—
698C3×Dic3—62no—
699C3×Dic3—62no—
700C3×Dic3—62no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—271no—
722#126—271no—
723#124—91no—
724#124—271no—
725#123—271no—
726#123—271no—
727C22⋊Q8—271no—
728#121—91no—
729#121—271no—
730#121—271no—
731#120—271no—
732#120—271no—
733C4×D4—91no—
734C4×D4—271no—
735C2×C22⋊C4—271no—
736C33#53811yescharacteristic, complemented, Sylow
737C23×C3—21no—
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—41no—
741C23×C3—91no—
742C23×C3—91no—
743C23×C3—91no—
744C23×C3—91no—
745C23×C3C2×D3211yescharacteristic
746C23×C3C2×D3211yescharacteristic
747C23×C3C2×D3211yescharacteristic
748C22×D3—31no—
749C22×D3—31no—
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—31no—
754C22×D3—31no—
755C22×D3—31no—
756C22×D3—61no—
757C22×D3—61no—
758C22×D3—61no—
759C22×D3—61no—
760C22×D3—182no—
761C22×D3—182no—
762C22×D3—182no—
763C22×D3—361no—
764C22×D3—361no—
765C22×D3—361no—
766C22×D3—361no—
767C22×D3—361no—
768C22×D3—361no—
769C3×Q8—361no—
770C3×D4—182no—
771C3×D4—361no—
772C3×D4—361no—
773C3×D4—361no—
774C3×D4—361no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—41no—
782C2×C3×C4—41no—
783C2×C3×C4—91no—
784C2×C3×C4—91no—
785C2×C3×C4—91no—
786C2×C3×C4—91no—
787C2×C3×C4—91no—
788C2×C3×C4—91no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4—361no—
792C2×C3×C4—361no—
793C2×C3×C4—361no—
794C2×C3×C4C2×D3211yescharacteristic
795C2×C3×C4C2×D3211yescharacteristic
796C2×C3×C4C2×D3211yescharacteristic
797C2×C3×C4C2×D3211yescharacteristic
798C2×C3×C4C2×D3211yescharacteristic
799C2×C3×C4C2×D3211yescharacteristic
800#67—62no—
801#67—62no—
802#67—64no—
803#67—121no—
804#67—121no—
805#67—121no—
806#67—121no—
807#67—121no—
808#67—121no—
809#67—122no—
810#67—122no—
811#67—122no—
812#67—182no—
813#67—182no—
814#67—361no—
815#67—361no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—31no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—61no—
833C2×Dic3—61no—
834C2×Dic3—61no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—61no—
838C2×Dic3—61no—
839C2×Dic3—61no—
840C2×Dic3—121no—
841C2×Dic3—121no—
842C2×Dic3—122no—
843C2×Dic3—361no—
844D12—121no—
845D12—121no—
846D12—122no—
847D12—182no—
848D12—361no—
849C4×D3—121no—
850C4×D3—121no—
851C4×D3—121no—
852C4×D3—121no—
853C4×D3—122no—
854C4×D3—122no—
855C4×D3—361no—
856C4×D3—361no—
857Dic6—121no—
858Dic6—121no—
859Dic6—122no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32—41no—
872C2×C32—41no—
873C2×C32—42no—
874C2×C32—41no—
875C2×C32—41no—
876C2×C32—81no—
877C2×C32—81no—
878C2×C32—82no—
879C2×C32C2×#23511yescharacteristic
880C2×C32#100411yescharacteristic
881C2×C32#100411yescharacteristic
882C2×C32#100411yescharacteristic
883C2×C32#100411yescharacteristic
884C2×C32D3×#4111yescharacteristic
885C2×C32D3×#4111yescharacteristic
886C2×C32#100911yescharacteristic
887C2×C32#100911yescharacteristic
888C3⋊D3—22no—
889C3⋊D3—41no—
890C3⋊D3—41no—
891C3⋊D3—41no—
892C3×D3—62no—
893C3×D3—62no—
894C3×D3—122no—
895C3×D3—122no—
896C3×D3—121no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—121no—
900C3×D3—121no—
901C3×D3—121no—
902C3×D3—241no—
903C3×D3—241no—
904C24—271no—
905C2×Q8—91no—
906C2×D4—91no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—271no—
912C2×D4—271no—
913C22×C4—91no—
914C22×C4—91no—
915C22×C4—91no—
916C22×C4—271no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—271no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4#111311yescharacteristic, complemented
937C42—91no—
938C42—91no—
939C22×C3—22no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—42no—
961C22×C3—41no—
962C22×C3—81no—
963C22×C3—81no—
964C22×C3—92no—
965C22×C3—181no—
966C22×C3—181no—
967C22×C3—181no—
968C22×C3—181no—
969C22×C3—181no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3—181no—
973C22×C3—181no—
974C22×C3—181no—
975C22×C3—181no—
976C22×C3C22×D3211yescharacteristic
977C22×C3C22×D3211yescharacteristic
978C22×C3C22×D3211yescharacteristic
979C2×D3—32no—
980C2×D3—32no—
981C2×D3—62no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—62no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—121no—
1006C2×D3—121no—
1007C2×D3—121no—
1008C2×D3—121no—
1009C2×D3—121no—
1010C2×D3—121no—
1011C2×D3—121no—
1012C2×D3—121no—
1013C2×D3—121no—
1014C2×D3—121no—
1015C2×D3—364no—
1016C2×D3—364no—
1017C2×D3—364no—
1018C3×C4—21no—
1019C3×C4—21no—
1020C3×C4—21no—
1021C3×C4—21no—
1022C3×C4—21no—
1023C3×C4—21no—
1024C3×C4—41no—
1025C3×C4—41no—
1026C3×C4—41no—
1027C3×C4—41no—
1028C3×C4—41no—
1029C3×C4—41no—
1030C3×C4—81no—
1031C3×C4—81no—
1032C3×C4—181no—
1033C3×C4—181no—
1034C3×C4—181no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039C3×C4—181no—
1040Dic3—62no—
1041Dic3—62no—
1042Dic3—62no—
1043Dic3—62no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—61no—
1056Dic3—61no—
1057Dic3—61no—
1058Dic3—61no—
1059Dic3—61no—
1060Dic3—121no—
1061Dic3—121no—
1062Dic3—121no—
1063Dic3—121no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#556011yescharacteristic, complemented
1069C32#561311yescharacteristic, complemented
1070C32#567811yescharacteristic, complemented
1071C23—91no—
1072C23—91no—
1073C23—91no—
1074C23—91no—
1075C23—542no—
1076C23—1081no—
1077C23—1081no—
1078C23C2×#111311yescharacteristic
1079Q8—361no—
1080D4—182no—
1081D4—361no—
1082D4—361no—
1083D4—361no—
1084D4—361no—
1085D4—542no—
1086D4—1081no—
1087C2×C4—91no—
1088C2×C4—91no—
1089C2×C4—91no—
1090C2×C4—91no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—361no—
1096C2×C4—361no—
1097C2×C4—361no—
1098C2×C4—1081no—
1099C2×C4C2×#111311yescharacteristic
1100C2×C4C2×#111311yescharacteristic
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—42no—
1111C2×C3—41no—
1112C2×C3—41no—
1113C2×C3—41no—
1114C2×C3—41no—
1115C2×C3—41no—
1116C2×C3—41no—
1117C2×C3—81no—
1118C2×C3—81no—
1119C2×C3—82no—
1120C2×C3—182no—
1121C2×C3—361no—
1122C2×C3—361no—
1123C2×C3—361no—
1124C2×C3D3×#23511yescharacteristic
1125C2×C3D3×#23511yescharacteristic
1126C2×C3#6430611yescharacteristic
1127C2×C3#6431311yescharacteristic
1128C2×C3#6431311yescharacteristic
1129C2×C3#6431411yescharacteristic
1130C2×C3#6431411yescharacteristic
1131C2×C3#6431411yescharacteristic
1132C2×C3#6431411yescharacteristic
1133D3—62no—
1134D3—62no—
1135D3—122no—
1136D3—122no—
1137D3—121no—
1138D3—121no—
1139D3—121no—
1140D3—121no—
1141D3—121no—
1142D3—121no—
1143D3—241no—
1144D3—241no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—92no—
1149C22—181no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22—181no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—181no—
1158C22—181no—
1159C22—181no—
1160C22—1084no—
1161C22C22×#111311yescharacteristic
1162C4—21no—
1163C4—21no—
1164C4—181no—
1165C4—181no—
1166C4—181no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—181no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059429711yescharacteristic, complemented
1177C3#1059429811yescharacteristic, complemented
1178C3#1059430611yescharacteristic, complemented
1179C2—41no—
1180C2—182no—
1181C2—361no—
1182C2—361no—
1183C2—361no—
1184C2#1172461811yescharacteristic
1185C2#1172462311yescharacteristic
1186C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64094C2semidirect
2. C3×#64093C2semidirect
3. C3×#64090C2semidirect
4. #11723729C2semidirect
5. #11723725C2semidirect
6. #11723720C2semidirect
7. #11723717C2semidirect
8. #11723701C2semidirect
9. #11723700C2semidirect
10. #11723694C2semidirect
11. C4×#6295C2semidirect
12. #11723688C2semidirect
13. #11723677C2semidirect
14. #11723676C2semidirect
15. #11723676C2semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×#634C22semidirect
32. C33×C22⋊C4C22semidirect
33. C3×#3757C22semidirect
38. C3×#3750C22semidirect
39. C3×#3750C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
44. #88815C22semidirect
45. #88815C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #64094D3semidirect
55. #64093D3semidirect
56. #64090D3semidirect
141. C2×#638C2×D3semidirect
142. C22×C3⋊Dic3C2×D3semidirect
145. C2×C4×C3⋊D3C2×D3semidirect
146. C2×#634C2×D3semidirect
187. C32×C22⋊C4C2×D3semidirect
188. C32×C22⋊C4C2×D3semidirect
189. C32×C22⋊C4C2×D3semidirect
190. #3757C2×D3semidirect
195. #3750C2×D3semidirect
196. #3750C2×D3semidirect
197. C4×C3⋊Dic3C2×D3semidirect
198. C4×C3⋊Dic3C2×D3semidirect
528. C3×C22⋊C4D32semidirect
529. C3×C22⋊C4D32semidirect
530. C3×C22⋊C4D32semidirect
736. C33#538semidirect
936. C22⋊C4#1113semidirect
1068. C32#5560semidirect
1069. C32#5613semidirect
1070. C32#5678semidirect
1176. C3#10594297semidirect
1177. C3#10594298semidirect
1178. C3#10594306semidirect

Maximal subgroups

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

subgroupindex
C3×#640942
C3×#640932
C3×#640902
#117237292
#117237252
#117237202
#117237172
#117237012
#117237002
#117236942
C4×#62952
#117236882
#117236772
#117236762
#105943063
#105942983
#105942973