Finite Group Databasebeta

← #13168753

Subgroups — #13168753

Order 1728.

1136 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723495C211yesmaximal, characteristic, complemented
3#11723479C211yesmaximal, characteristic, complemented
4#11723414C211yesmaximal, characteristic, complemented
5C3×#63905C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63858C211yesmaximal, characteristic, complemented
8#11723028C211yesmaximal, characteristic, complemented
9#11723012C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722980C211yesmaximal, characteristic, complemented
12#11722971C211yesmaximal, characteristic, complemented
13#11722958C211yesmaximal, characteristic
14#11722932C211yesmaximal, characteristic, complemented
15#11722924C211yesmaximal, characteristic, complemented
16#10594987—31nomaximal
17#10594541—31nomaximal
18#10594128—31nomaximal
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×C3×#625C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28#88859C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic
34#88815C2211yescharacteristic
35#88815C2211yescharacteristic
36#88815C2211yescharacteristic
37#88813C2211yescharacteristic
38#88807C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64138—31no—
55#64105—31no—
56#64095—31no—
57C3×#929—31no—
58C2×C3×C4⋊Dic3—31no—
59C3×#898—31no—
60C3×D3×C4⋊C4—31no—
61C3×#883—31no—
62C3×#879—31no—
63#63982—31no—
64#63978—31no—
65#63975—31no—
66#67⋊Dic3—31no—
67Dic3×#67—31no—
68#63971—31no—
69#63964—31no—
70#63952—31no—
71#63906—31no—
72#63905D311yescharacteristic, complemented
73C4×#626—31no—
74#63899—31no—
75#63896—31no—
76#63895—31no—
77#63895—31no—
78#63895—61no—
79#63893—31no—
80#63890—31no—
81#63890—31no—
82#63890—61no—
83D3×C4⋊Dic3D311yescharacteristic, complemented
84#63880—31no—
85#63879—31no—
86#63869—31no—
87#63867—31no—
88#63858D311yescharacteristic, complemented
89#63857—31no—
90#63854—31no—
91#63853—31no—
92#63850—31no—
93#63850—31no—
94#63850—61no—
95#63848—31no—
96#63848—31no—
97#63848—31no—
98#63847—31no—
99#63846—31no—
100#63846—31no—
101#63845—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
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×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118#6293—41no—
119#6291—22no—
120#6291—41no—
121#6289—41no—
122D3×C3⋊Dic3—41no—
123C3×#625—22no—
124C3×D3×Dic3—41no—
125C3×D3×Dic3—41no—
126#5707—91no—
127#5665—91no—
128#5515—91no—
129C22×C32×C4—31no—
130C2×#638—31no—
131C2×#638—31no—
132C22×C3⋊Dic3—31no—
133C2×C4×C3⋊D3—31no—
134C2×#634—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3C2×D311yescharacteristic
143C2×C3×C4×D3C2×D311yescharacteristic
144C2×#627—31no—
145C2×#627—31no—
146C2×#627—61no—
147C2×#626—31no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—61no—
152C2×#626—61no—
153C2×#625C2×D311yescharacteristic
154C2×#624—31no—
155C2×#624—31no—
156C2×#624—61no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—61no—
160C2×D3×Dic3C2×D311yescharacteristic
161C2×D3×Dic3C2×D311yescharacteristic
162C32×C4⋊C4—31no—
163C32×C22⋊C4—31no—
164#3757—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—61no—
172#3752—61no—
173#3752—61no—
174#3752—121no—
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)C2×D311yescharacteristic
177#3750—31no—
178#3750—31no—
179#3750C2×D311yescharacteristic
180#3750C2×D311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×(C2×D3)⋊C4—21no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4C2×D311yescharacteristic
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×C4⋊Dic3—21no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—61no—
200C3×C4⋊Dic3C2×D311yescharacteristic
201C3×C4⋊Dic3C2×D311yescharacteristic
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×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235Dic3⋊Dic3C2×D311yescharacteristic
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—61no—
243#3722—61no—
244#3722—61no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3#4112yes—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#126—91no—
279C3×#123—91no—
280C2×C3×C4⋊C4—91no—
281#939—91no—
282D4×Dic3—91no—
283#930—91no—
284#929—31no—
285#929—91no—
286#929—91no—
287#929—181no—
288C4×#67—91no—
289C4×#67—91no—
290C2×C4⋊Dic3—31no—
291#924—91no—
292#898—31no—
293#898—91no—
294#898—91no—
295#898—91no—
296#897—91no—
297#897—91no—
298#896—91no—
299#896—91no—
300#896—91no—
301#896—181no—
302#894—91no—
303#894—91no—
304#894—91no—
305D3×C4⋊C4—31no—
306#890—91no—
307#890—91no—
308#889—91no—
309#889—91no—
310#889—91no—
311#886—91no—
312#886—91no—
313#886—181no—
314#884—91no—
315#883—31no—
316#883—91no—
317#883—91no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320#879—31no—
321#878—91no—
322#878—91no—
323#878—91no—
324C4×D12—91no—
325#870—91no—
326C23×C32—31no—
327C23×C32—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—31no—
330C22×C3⋊D3—31no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—61no—
333C22×C3⋊D3—61no—
334C22×C3⋊D3—121no—
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3C22×D311yescharacteristic
338C22×C3×D3C22×D311yescharacteristic
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—31no—
348C2×C32×C4—41no—
349C2×C32×C4—62no—
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353#638—62no—
354#638—121no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3—121no—
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C4×C3⋊D3—121no—
370#634—121no—
371C3×#67—62no—
372C3×#67—62no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
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—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—121no—
396C2×C3×Dic3—121no—
397C2×C3×Dic3C22×D311yescharacteristic
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
405C3×C4×D3—22no—
406C3×C4×D3—22no—
407C3×C4×D3—42no—
408C3×C4×D3—121no—
409C3×C4×D3—121no—
410#627—121no—
411#627—121no—
412#627—122no—
413#626—62no—
414#626—62no—
415#626—122no—
416#626—121no—
417#626—121no—
418#626—122no—
419#625—22no—
420#624—121no—
421#624—121no—
422#624—122no—
423D3×Dic3—41no—
424D3×Dic3—41no—
425D3×Dic3—121no—
426D3×Dic3—121no—
427D3×Dic3—122no—
428#539—271noSylow
429C2×C33C2×#4111yescharacteristic
430C2×C33H(5,𝔽2)11yescharacteristic
431C2×C332−1+411yescharacteristic
432C3⋊(C3⋊D3)—41no—
433C32×D3—22no—
434C32×D3—41no—
435C2×C3×D4—91no—
436C22×C3×C4—31no—
437C22×C3×C4—31no—
438C22×C3×C4—61no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—31no—
443C2×#67—91no—
444C2×#67—91no—
445C2×#67—91no—
446C2×#67—91no—
447C2×#67—181no—
448C2×#67—181no—
449C22×Dic3—31no—
450C22×Dic3—31no—
451C22×Dic3—91no—
452C22×Dic3—91no—
453C22×Dic3—181no—
454C2×D12—91no—
455C2×D12—91no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—181no—
463C2×C4×D3D3211yescharacteristic
464C2×Dic6—91no—
465C2×Dic6—91no—
466C2×Dic6—91no—
467C2×Dic6—181no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—61no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C22⋊C4—31no—
479C3×C22⋊C4—31no—
480C3×C22⋊C4—61no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C42—91no—
486#217—31no—
487#217—31no—
488#217—31no—
489#217—31no—
490#217—91no—
491#217—91no—
492#217—181no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—91no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
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—181no—
511(C2×D3)⋊C4—181no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4—181no—
515(C2×D3)⋊C4—181no—
516(C2×D3)⋊C4—361no—
517(C2×D3)⋊C4D3211yescharacteristic
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—31no—
521C4⋊Dic3—31no—
522C4⋊Dic3—31no—
523C4⋊Dic3—31no—
524C4⋊Dic3—61no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—91no—
528C4⋊Dic3—91no—
529C4⋊Dic3—91no—
530C4⋊Dic3—91no—
531C4⋊Dic3—181no—
532C4⋊Dic3D3211yescharacteristic
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—61no—
542Dic3⋊C4—61no—
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—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—181no—
556Dic3⋊C4—181no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—32no—
566C22×C32—41no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32—61no—
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C22×C32C23×D311yescharacteristic
575C2×C3⋊D3—61no—
576C2×C3⋊D3—62no—
577C2×C3⋊D3—61no—
578C2×C3⋊D3—61no—
579C2×C3⋊D3—61no—
580C2×C3⋊D3—61no—
581C2×C3⋊D3—61no—
582C2×C3⋊D3—61no—
583C2×C3⋊D3—61no—
584C2×C3⋊D3—61no—
585C2×C3⋊D3—121no—
586C2×C3⋊D3—121no—
587C2×C3⋊D3—122no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—121no—
594C2×C3⋊D3—241no—
595C2×C3⋊D3—241no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—22no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—21no—
607C2×C3×D3—22no—
608C2×C3×D3—41no—
609C2×C3×D3—41no—
610C2×C3×D3—41no—
611C2×C3×D3—41no—
612C2×C3×D3#23512yes—
613C2×C3×D3#23712yes—
614C32×C4—21no—
615C32×C4—21no—
616C32×C4—21no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—61no—
621C32×C4—61no—
622C32×C4—61no—
623C32×C4—61no—
624C32×C4—81no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—61no—
632C3⋊Dic3—61no—
633C3⋊Dic3—61no—
634C3⋊Dic3—121no—
635C3⋊Dic3—121no—
636C3⋊Dic3—121no—
637C3⋊Dic3—241no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—41no—
650C3×Dic3—62no—
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—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—121no—
664C3×Dic3—121no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668#126—91no—
669#126—271no—
670#125—271no—
671#125—271no—
672#123—91no—
673#123—271no—
674#123—271no—
675#123—271no—
676C22⋊Q8—271no—
677C22⋊Q8—271no—
678C22⋊Q8—271no—
679#121—271no—
680C4×D4—271no—
681C4×D4—271no—
682C2×C4⋊C4—91no—
683C33#53911yescharacteristic, complemented, Sylow
684C23×C3—31no—
685C23×C3—31no—
686C23×C3—31no—
687C23×C3—31no—
688C23×C3—61no—
689C23×C3—61no—
690C22×D3—91no—
691C22×D3—91no—
692C22×D3—91no—
693C22×D3—181no—
694C22×D3—181no—
695C22×D3—181no—
696C22×D3—361no—
697C22×D3C2×D3211yescharacteristic
698C22×D3C2×D3211yescharacteristic
699C3×D4—182no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—41no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—62no—
717C2×C3×C4—62no—
718C2×C3×C4—91no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—122no—
725C2×C3×C4—361no—
726C2×C3×C4—361no—
727C2×C3×C4C2×D3211yescharacteristic
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730#67—62no—
731#67—62no—
732#67—182no—
733#67—182no—
734#67—362no—
735#67—361no—
736#67—361no—
737#67—362no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—91no—
757C2×Dic3—91no—
758C2×Dic3—91no—
759C2×Dic3—121no—
760C2×Dic3—121no—
761C2×Dic3—181no—
762C2×Dic3—181no—
763C2×Dic3—181no—
764C2×Dic3—361no—
765C2×Dic3—361no—
766C2×Dic3—361no—
767C2×Dic3—362no—
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770C2×Dic3C2×D3211yescharacteristic
771C2×Dic3C2×D3211yescharacteristic
772D12—182no—
773D12—361no—
774C4×D3—22no—
775C4×D3—121no—
776C4×D3—121no—
777C4×D3—361no—
778C4×D3—361no—
779C4×D3—361no—
780C4×D3—362no—
781C4×D3—361no—
782Dic6—361no—
783Dic6—361no—
784Dic6—361no—
785Dic6—362no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—41no—
796C2×C32—41no—
797C2×C32—41no—
798C2×C32—62no—
799C2×C32—121no—
800C2×C32C2×#23511yescharacteristic
801C2×C32C2×#23711yescharacteristic
802C2×C32#100411yescharacteristic
803C2×C32#100711yescharacteristic
804C2×C32D3×#4111yescharacteristic
805C2×C32#100911yescharacteristic
806C2×C32#100911yescharacteristic
807C2×C32#101011yescharacteristic
808C2×C32#101011yescharacteristic
809C3⋊D3—121no—
810C3⋊D3—122no—
811C3⋊D3—121no—
812C3⋊D3—121no—
813C3⋊D3—241no—
814C3⋊D3—241no—
815C3⋊D3—242no—
816C3×D3—22no—
817C3×D3—22no—
818C3×D3—42no—
819C3×D3—42no—
820C3×D3—41no—
821C3×D3—41no—
822C2×Q8—271no—
823C2×D4—91no—
824C2×D4—271no—
825C2×D4—271no—
826C22×C4—31no—
827C22×C4—91no—
828C22×C4—91no—
829C22×C4—271no—
830C22×C4—271no—
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—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C22⋊C4—31no—
846C22⋊C4—91no—
847C22⋊C4—91no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C42—91no—
856C42—271no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—32no—
861C22×C3—32no—
862C22×C3—41no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—61no—
866C22×C3—61no—
867C22×C3—61no—
868C22×C3—61no—
869C22×C3—61no—
870C22×C3—61no—
871C22×C3—61no—
872C22×C3—61no—
873C22×C3—61no—
874C22×C3—61no—
875C22×C3—121no—
876C22×C3—121no—
877C22×C3—121no—
878C22×C3—121no—
879C22×C3C22×D3211yescharacteristic
880C22×C3C22×D3211yescharacteristic
881C22×C3C22×D3211yescharacteristic
882C2×D3—21no—
883C2×D3—21no—
884C2×D3—21no—
885C2×D3—21no—
886C2×D3—21no—
887C2×D3—182no—
888C2×D3—181no—
889C2×D3—181no—
890C2×D3—181no—
891C2×D3—181no—
892C2×D3—181no—
893C2×D3—181no—
894C2×D3—181no—
895C2×D3—181no—
896C2×D3—181no—
897C2×D3—361no—
898C2×D3—361no—
899C2×D3—361no—
900C2×D3—361no—
901C2×D3—361no—
902C2×D3—361no—
903C2×D3—361no—
904C2×D3—361no—
905C2×D3—362no—
906C2×D3—721no—
907C2×D3—721no—
908C2×D3#380412yes—
909C3×C4—21no—
910C3×C4—21no—
911C3×C4—21no—
912C3×C4—41no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—81no—
924C3×C4—121no—
925C3×C4—121no—
926C3×C4—121no—
927C3×C4—121no—
928C3×C4—181no—
929C3×C4—181no—
930C3×C4—181no—
931C3×C4—181no—
932C3×C4—181no—
933C3×C4—181no—
934Dic3—21no—
935Dic3—21no—
936Dic3—21no—
937Dic3—21no—
938Dic3—62no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—121no—
952Dic3—121no—
953Dic3—121no—
954Dic3—121no—
955Dic3—121no—
956Dic3—181no—
957Dic3—181no—
958Dic3—181no—
959Dic3—361no—
960Dic3—361no—
961Dic3—361no—
962Dic3—721no—
963C32—21no—
964C32—21no—
965C32—21no—
966C32—41no—
967C32#551511yescharacteristic, complemented
968C32#566511yescharacteristic, complemented
969C32#570711yescharacteristic, complemented
970C23—31no—
971C23—31no—
972C23—271no—
973Q8—1081no—
974D4—182no—
975D4—542no—
976D4—1081no—
977C2×C4—31no—
978C2×C4—31no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—62no—
982C2×C4—91no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—91no—
988C2×C4—271no—
989C2×C4—361no—
990C2×C4—361no—
991C2×C4—1081no—
992C2×C4—1081no—
993C2×C4D3311yescharacteristic
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—41no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—62no—
1007C2×C3—62no—
1008C2×C3—122no—
1009C2×C3—122no—
1010C2×C3—121no—
1011C2×C3—121no—
1012C2×C3#6429711yescharacteristic
1013C2×C3D3×#23511yescharacteristic
1014C2×C3#6430711yescharacteristic
1015C2×C3#6430811yescharacteristic
1016C2×C3#6430911yescharacteristic
1017C2×C3D3×#23711yescharacteristic
1018C2×C3#6431411yescharacteristic
1019C2×C3#6431511yescharacteristic
1020C2×C3C2×#380411yescharacteristic
1021D3—22no—
1022D3—41no—
1023D3—362no—
1024D3—361no—
1025D3—361no—
1026D3—361no—
1027D3—721no—
1028D3—721no—
1029D3—722no—
1030C22—32no—
1031C22—61no—
1032C22—61no—
1033C22—61no—
1034C22—61no—
1035C22—61no—
1036C22—541no—
1037C22—541no—
1038C22—541no—
1039C22C2×D3311yescharacteristic
1040C4—21no—
1041C4—61no—
1042C4—61no—
1043C4—61no—
1044C4—61no—
1045C4—181no—
1046C4—181no—
1047C4—181no—
1048C4—181no—
1049C4—181no—
1050C4—181no—
1051C4—541no—
1052C3—21no—
1053C3—21no—
1054C3—21no—
1055C3—41no—
1056C3#1059412811yescharacteristic, complemented
1057C3#1059454111yescharacteristic, complemented
1058C3#1059498711yescharacteristic, complemented
1059C2—62no—
1060C2—121no—
1061C2—1081no—
1062C2#1172438411yescharacteristic
1063C2#1172439311yescharacteristic
1064C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722958C2
hypercenterC2×C4D33
hypocenterC33#539
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. #11723495C2semidirect
3. #11723479C2semidirect
4. #11723414C2semidirect
5. C3×#63905C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63858C2semidirect
8. #11723028C2semidirect
9. #11723012C2semidirect
10. #11722996C2semidirect
11. #11722980C2semidirect
12. #11722971C2semidirect
14. #11722932C2semidirect
15. #11722924C2semidirect
72. #63905D3semidirect
83. D3×C4⋊Dic3D3semidirect
88. #63858D3semidirect
683. C33#539semidirect
967. C32#5515semidirect
968. C32#5665semidirect
969. C32#5707semidirect
1056. C3#10594128semidirect
1057. C3#10594541semidirect
1058. C3#10594987semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117234952
#117234792
#117234142
C3×#639052
C3×D3×C4⋊Dic32
C3×#638582
#117230282
#117230122
#117229962
#117229802
#117229712
#117229582
#117229322
#117229242
#105949873
#105945413
#105941283