Finite Group Databasebeta

← #13168281

Subgroups — #13168281

Order 1728.

1154 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723679C211yesmaximal, characteristic, complemented
2#11723462C211yesmaximal, characteristic
3#11723452C211yesmaximal, characteristic, complemented
4#11723442C211yesmaximal, characteristic, complemented
5C3×#63878C211yesmaximal, characteristic, complemented
6C3×#63877C211yesmaximal, characteristic, complemented
7C3×#63867C211yesmaximal, characteristic, complemented
8#11723021C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11723016C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic
12#11722987C211yesmaximal, characteristic
13#11722980C211yesmaximal, characteristic, complemented
14#11722942C211yesmaximal, characteristic, complemented
15D3×#3724C211yesmaximal, characteristic, complemented
16#10594408—31nomaximal
17#10594046—31nomaximal
18#10593918—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C3×#3750C2211yescharacteristic
26C3×#3750C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C32×(C2×D3)⋊C4C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64090—31no—
56#64081—31no—
57C3×#892—31no—
58C3×#889—31no—
59C3×#877—31no—
60C3×#877—31no—
61C3×#872—31no—
62C3×#870—31no—
63#63982—31no—
64C2×#3724—31no—
65#63966—31no—
66#63966—31no—
67C4×#627—31no—
68#63899—31no—
69#63896—31no—
70#63890—31no—
71#63890—31no—
72#63881—31no—
73#63881—31no—
74#63881—61no—
75#63878D311yescharacteristic, complemented
76#63877D311yescharacteristic, complemented
77D3×Dic3⋊C4—31no—
78D3×Dic3⋊C4—31no—
79#63874—31no—
80#63874—31no—
81#63874—61no—
82#63870—31no—
83#63870—31no—
84#63868—31no—
85#63868—31no—
86#63868—31no—
87#63868—31no—
88#63867—31no—
89#63867—31no—
90#63867D311yescharacteristic, complemented
91#63865—31no—
92#63865—31no—
93#63865—61no—
94#63850—31no—
95#63850—31no—
96#63848—31no—
97#63848—31no—
98#63847—31no—
99#63847—31no—
100#63844—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#6291—22no—
120D3×C3⋊Dic3—22no—
121C3×D3×Dic3—22no—
122C3×D3×Dic3—22no—
123#5693—91no—
124#5531—91no—
125#5531—91no—
126C2×#638—31no—
127C22×C3⋊Dic3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—61no—
132C2×C4×C3⋊D3—61no—
133C2×C4×C3⋊D3—61no—
134C2×C4×C3⋊D3—121no—
135C2×#634—31no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×#627—31no—
141C2×#627—31no—
142C2×#627—61no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—61no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—61no—
149C2×D3×Dic3C2×D311yescharacteristic
150C2×D3×Dic3C2×D311yescharacteristic
151C32×C4⋊C4—31no—
152C32×C22⋊C4—31no—
153C32×C42—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750C2×D311yescharacteristic
163#3750C2×D311yescharacteristic
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3C2×D311yescharacteristic
166C3×#217—31no—
167C3×#217—31no—
168C3×(C2×D3)⋊C4—21no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4C2×D311yescharacteristic
172C3×(C2×D3)⋊C4C2×D311yescharacteristic
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×Dic3⋊C4—21no—
178C3×Dic3⋊C4—31no—
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—31no—
190C3×Dic3⋊C4—61no—
191C3×Dic3⋊C4—61no—
192C3×Dic3⋊C4C2×D311yescharacteristic
193C3×Dic3⋊C4C2×D311yescharacteristic
194C3×C4×Dic3—21no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—61no—
202C3×C4×Dic3C2×D311yescharacteristic
203C3×C4×Dic3C2×D311yescharacteristic
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—61no—
215#3724—61no—
216#3724—61no—
217#3724C2×D311yescharacteristic
218#3724C2×D311yescharacteristic
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—61no—
242#3722—61no—
243#3722—61no—
244#3722—61no—
245#3722—61no—
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3⋊(C3⋊D3)—21no—
255C2×C3⋊(C3⋊D3)—21no—
256C2×C3⋊(C3⋊D3)—21no—
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3#4112yes—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)#4112yes—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C3×#125—91no—
274C3×#117—91no—
275C3×#117—91no—
276#929—91no—
277#929—91no—
278C2×Dic3⋊C4—91no—
279C2×Dic3⋊C4—91no—
280#898—91no—
281#898—91no—
282#898—91no—
283#898—91no—
284#896—91no—
285#896—91no—
286#896—91no—
287#896—91no—
288#896—181no—
289#894—91no—
290#894—91no—
291#893—91no—
292#892—31no—
293D3×C4⋊C4—91no—
294#889—31no—
295#889—91no—
296#889—91no—
297#889—91no—
298#889—91no—
299#889—91no—
300#887—91no—
301#886—91no—
302#886—91no—
303#67⋊C4—91no—
304#67⋊C4—91no—
305#67⋊C4—181no—
306#878—91no—
307#878—91no—
308#877—31no—
309#877—31no—
310#876—91no—
311#876—91no—
312#872—31no—
313#872—91no—
314#872—91no—
315#872—91no—
316#872—181no—
317#870—31no—
318#870—91no—
319C4×Dic6—91no—
320C4×Dic6—91no—
321C23×C32—31no—
322C22×C3⋊D3—31no—
323C22×C3⋊D3—31no—
324C22×C3⋊D3—31no—
325C22×C3⋊D3—61no—
326C22×C3⋊D3—61no—
327C22×C3⋊D3—61no—
328C22×C3⋊D3—121no—
329C22×C3×D3—21no—
330C22×C3×D3C22×D311yescharacteristic
331C22×C3×D3C22×D311yescharacteristic
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—41no—
341C2×C32×C4C22×D311yescharacteristic
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344#638—62no—
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—62no—
352C2×C3⋊Dic3—121no—
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C4×C3⋊D3—62no—
360C4×C3⋊D3—62no—
361C4×C3⋊D3—62no—
362C4×C3⋊D3—64no—
363C4×C3⋊D3—122no—
364C4×C3⋊D3—122no—
365C4×C3⋊D3—124no—
366#634—62no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—62no—
391C2×C3×Dic3—62no—
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C3×C4×D3—62no—
403C3×C4×D3—62no—
404#627—62no—
405#627—62no—
406#627—122no—
407#626—64no—
408#626—62no—
409#626—62no—
410D3×Dic3—22no—
411D3×Dic3—22no—
412D3×Dic3—62no—
413D3×Dic3—62no—
414D3×Dic3—122no—
415#552—271noSylow
416C2×C33C2×#4111yescharacteristic
417C2×C33C2×#4111yescharacteristic
418C2×C332−1+411yescharacteristic
419C3⋊(C3⋊D3)—41no—
420C32×D3—22no—
421C22×C3×C4—91no—
422C22×C3×C4—91no—
423C2×#67—91no—
424C2×#67—91no—
425C2×#67—181no—
426C22×Dic3—31no—
427C22×Dic3—31no—
428C22×Dic3—91no—
429C22×Dic3—91no—
430C22×Dic3—181no—
431C2×D12—91no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—181no—
439C2×C4×D3—181no—
440C2×C4×D3—181no—
441C2×C4×D3—361no—
442C2×Dic6—91no—
443C2×Dic6—91no—
444C2×Dic6—91no—
445C2×Dic6—181no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—61no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C22⋊C4—31no—
458C3×C22⋊C4—31no—
459C3×C22⋊C4—61no—
460C3×C22⋊C4—91no—
461C3×C22⋊C4—91no—
462C3×C42—31no—
463C3×C42—31no—
464C3×C42—61no—
465C3×C42—91no—
466C3×C42—91no—
467C3×C42—91no—
468#217—31no—
469#217—31no—
470(C2×D3)⋊C4—31no—
471(C2×D3)⋊C4—31no—
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—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—181no—
488(C2×D3)⋊C4—181no—
489(C2×D3)⋊C4—181no—
490(C2×D3)⋊C4—181no—
491(C2×D3)⋊C4—181no—
492(C2×D3)⋊C4D3211yescharacteristic
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—91no—
498C4⋊Dic3—91no—
499C4⋊Dic3—91no—
500C4⋊Dic3—91no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—61no—
514Dic3⋊C4—61no—
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—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—181no—
533Dic3⋊C4—181no—
534Dic3⋊C4—181no—
535Dic3⋊C4D3211yescharacteristic
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—31no—
541C4×Dic3—31no—
542C4×Dic3—61no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C4×Dic3—91no—
546C4×Dic3—181no—
547C4×Dic3D3211yescharacteristic
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—32no—
552C22×C32—41no—
553C22×C32—61no—
554C22×C32—61no—
555C22×C32C23×D311yescharacteristic
556C22×C32C23×D311yescharacteristic
557C22×C32C23×D311yescharacteristic
558C2×C3⋊D3—61no—
559C2×C3⋊D3—61no—
560C2×C3⋊D3—61no—
561C2×C3⋊D3—62no—
562C2×C3⋊D3—62no—
563C2×C3⋊D3—62no—
564C2×C3⋊D3—61no—
565C2×C3⋊D3—61no—
566C2×C3⋊D3—61no—
567C2×C3⋊D3—61no—
568C2×C3⋊D3—61no—
569C2×C3⋊D3—61no—
570C2×C3⋊D3—121no—
571C2×C3⋊D3—121no—
572C2×C3⋊D3—121no—
573C2×C3⋊D3—121no—
574C2×C3⋊D3—121no—
575C2×C3⋊D3—121no—
576C2×C3⋊D3—122no—
577C2×C3⋊D3—122no—
578C2×C3⋊D3—122no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—22no—
584C2×C3×D3—41no—
585C2×C3×D3—41no—
586C2×C3×D3#23512yes—
587C2×C3×D3#23512yes—
588C32×C4—21no—
589C32×C4—22no—
590C32×C4—21no—
591C32×C4—21no—
592C32×C4—41no—
593C32×C4—41no—
594C32×C4—42no—
595C32×C4—61no—
596C32×C4—61no—
597C32×C4—61no—
598C32×C4—61no—
599C32×C4—61no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—21no—
605C3⋊Dic3—21no—
606C3⋊Dic3—32no—
607C3⋊Dic3—32no—
608C3⋊Dic3—32no—
609C3⋊Dic3—62no—
610C3⋊Dic3—62no—
611C3⋊Dic3—62no—
612C3⋊Dic3—122no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—21no—
621C3×Dic3—21no—
622C3×Dic3—21no—
623C3×Dic3—41no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—41no—
627C3×Dic3—41no—
628C3×Dic3—62no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—61no—
638C3×Dic3—61no—
639C3×Dic3—61no—
640C3×Dic3—61no—
641C3×Dic3—121no—
642C3×Dic3—121no—
643C3×Dic3—121no—
644C3×Dic3—121no—
645C3×Dic3—121no—
646#126—271no—
647#126—271no—
648#125—91no—
649#125—271no—
650#125—271no—
651#123—271no—
652#123—271no—
653C22⋊Q8—271no—
654C22⋊Q8—271no—
655C4×Q8—271no—
656C4×D4—271no—
657#117—91no—
658#117—91no—
659#117—271no—
660C2×C4⋊C4—271no—
661C33#55211yescharacteristic, complemented, Sylow
662C23×C3—31no—
663C23×C3—31no—
664C23×C3—61no—
665C22×D3—91no—
666C22×D3—91no—
667C22×D3—91no—
668C22×D3—181no—
669C22×D3—181no—
670C22×D3—181no—
671C22×D3—361no—
672C22×D3C2×D3211yescharacteristic
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—31no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—41no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—91no—
693C2×C3×C4—91no—
694C2×C3×C4—91no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—182no—
699C2×C3×C4—182no—
700C2×C3×C4C2×D3211yescharacteristic
701C2×C3×C4C2×D3211yescharacteristic
702C2×C3×C4C2×D3211yescharacteristic
703#67—182no—
704#67—182no—
705#67—184no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—91no—
727C2×Dic3—91no—
728C2×Dic3—91no—
729C2×Dic3—181no—
730C2×Dic3—181no—
731C2×Dic3—181no—
732C2×Dic3—182no—
733C2×Dic3—182no—
734C2×Dic3—361no—
735C2×Dic3—362no—
736C2×Dic3C2×D3211yescharacteristic
737C2×Dic3C2×D3211yescharacteristic
738C2×Dic3C2×D3211yescharacteristic
739C2×Dic3C2×D3211yescharacteristic
740C2×Dic3C2×D3211yescharacteristic
741D12—182no—
742C4×D3—62no—
743C4×D3—62no—
744C4×D3—182no—
745C4×D3—182no—
746C4×D3—182no—
747C4×D3—182no—
748C4×D3—184no—
749C4×D3—362no—
750C4×D3—362no—
751C4×D3—364no—
752Dic6—182no—
753Dic6—182no—
754Dic6—182no—
755Dic6—362no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—21no—
760C2×C32—21no—
761C2×C32—21no—
762C2×C32—21no—
763C2×C32—21no—
764C2×C32—21no—
765C2×C32—41no—
766C2×C32—41no—
767C2×C32—41no—
768C2×C32—62no—
769C2×C32C2×#23511yescharacteristic
770C2×C32C2×#23511yescharacteristic
771C2×C32#100711yescharacteristic
772C2×C32D3×#4111yescharacteristic
773C2×C32D3×#4111yescharacteristic
774C2×C32D3×#4111yescharacteristic
775C2×C32D3×#4111yescharacteristic
776C2×C32#101011yescharacteristic
777C2×C32#101011yescharacteristic
778C3⋊D3—122no—
779C3⋊D3—122no—
780C3⋊D3—122no—
781C3⋊D3—124no—
782C3⋊D3—121no—
783C3⋊D3—121no—
784C3⋊D3—121no—
785C3×D3—22no—
786C3×D3—22no—
787C3×D3—42no—
788C2×Q8—271no—
789C2×D4—271no—
790C22×C4—91no—
791C22×C4—91no—
792C22×C4—271no—
793C22×C4—271no—
794C4⋊C4—31no—
795C4⋊C4—91no—
796C4⋊C4—91no—
797C4⋊C4—91no—
798C4⋊C4—91no—
799C4⋊C4—91no—
800C4⋊C4—91no—
801C4⋊C4—91no—
802C4⋊C4—91no—
803C4⋊C4—271no—
804C4⋊C4—271no—
805C4⋊C4—271no—
806C4⋊C4—271no—
807C4⋊C4—271no—
808C4⋊C4—271no—
809C4⋊C4—271no—
810C22⋊C4—31no—
811C22⋊C4—91no—
812C22⋊C4—91no—
813C22⋊C4—271no—
814C22⋊C4—271no—
815C22⋊C4—271no—
816C22⋊C4—271no—
817C22⋊C4—271no—
818C42—31no—
819C42—91no—
820C42—91no—
821C42—91no—
822C42—271no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—32no—
827C22×C3—32no—
828C22×C3—41no—
829C22×C3—62no—
830C22×C3—61no—
831C22×C3—61no—
832C22×C3—61no—
833C22×C3—61no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3C22×D3211yescharacteristic
837C22×C3C22×D3211yescharacteristic
838C22×C3C22×D3211yescharacteristic
839C2×D3—21no—
840C2×D3—21no—
841C2×D3—182no—
842C2×D3—182no—
843C2×D3—182no—
844C2×D3—181no—
845C2×D3—181no—
846C2×D3—181no—
847C2×D3—181no—
848C2×D3—181no—
849C2×D3—181no—
850C2×D3—181no—
851C2×D3—181no—
852C2×D3—181no—
853C2×D3—361no—
854C2×D3—361no—
855C2×D3—361no—
856C2×D3—361no—
857C2×D3—361no—
858C2×D3—361no—
859C2×D3—362no—
860C2×D3—362no—
861C2×D3—362no—
862C2×D3#379812yes—
863C3×C4—22no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—21no—
867C3×C4—41no—
868C3×C4—41no—
869C3×C4—42no—
870C3×C4—61no—
871C3×C4—61no—
872C3×C4—61no—
873C3×C4—61no—
874C3×C4—61no—
875C3×C4—61no—
876C3×C4—61no—
877C3×C4—61no—
878C3×C4—61no—
879C3×C4—61no—
880C3×C4—121no—
881C3×C4—121no—
882C3×C4—121no—
883C3×C4—121no—
884C3×C4—121no—
885C3×C4—181no—
886C3×C4—181no—
887C3×C4—181no—
888C3×C4—181no—
889C3×C4—181no—
890C3×C4—181no—
891Dic3—21no—
892Dic3—21no—
893Dic3—21no—
894Dic3—21no—
895Dic3—21no—
896Dic3—62no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—61no—
901Dic3—61no—
902Dic3—61no—
903Dic3—61no—
904Dic3—61no—
905Dic3—61no—
906Dic3—61no—
907Dic3—61no—
908Dic3—61no—
909Dic3—92no—
910Dic3—92no—
911Dic3—92no—
912Dic3—121no—
913Dic3—121no—
914Dic3—121no—
915Dic3—121no—
916Dic3—121no—
917Dic3—182no—
918Dic3—182no—
919Dic3—182no—
920Dic3—362no—
921C32—21no—
922C32—21no—
923C32—21no—
924C32—41no—
925C32#553111yescharacteristic, complemented
926C32#553111yescharacteristic, complemented
927C32#569311yescharacteristic, complemented
928C23—31no—
929C23—271no—
930Q8—542no—
931D4—542no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—31no—
935C2×C4—31no—
936C2×C4—31no—
937C2×C4—91no—
938C2×C4—91no—
939C2×C4—91no—
940C2×C4—91no—
941C2×C4—91no—
942C2×C4—91no—
943C2×C4—182no—
944C2×C4—182no—
945C2×C4—271no—
946C2×C4—542no—
947C2×C4—542no—
948C2×C4D3311yescharacteristic
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—41no—
959C2×C3—41no—
960C2×C3—41no—
961C2×C3—62no—
962C2×C3—62no—
963C2×C3—122no—
964C2×C3#6429711yescharacteristic
965C2×C3C2×#379811yescharacteristic
966C2×C3D3×#23511yescharacteristic
967C2×C3D3×#23511yescharacteristic
968C2×C3#6430611yescharacteristic
969C2×C3#6430911yescharacteristic
970C2×C3#6431211yescharacteristic
971C2×C3#6431211yescharacteristic
972C2×C3#6431511yescharacteristic
973D3—22no—
974D3—362no—
975D3—362no—
976D3—362no—
977D3—364no—
978D3—361no—
979D3—361no—
980D3—361no—
981C22—32no—
982C22—61no—
983C22—61no—
984C22—541no—
985C22—541no—
986C22—541no—
987C22C2×D3311yescharacteristic
988C4—21no—
989C4—61no—
990C4—61no—
991C4—61no—
992C4—61no—
993C4—61no—
994C4—181no—
995C4—181no—
996C4—181no—
997C4—181no—
998C4—181no—
999C4—181no—
1000C4—272no—
1001C3—21no—
1002C3—21no—
1003C3—21no—
1004C3—41no—
1005C3#1059391811yescharacteristic, complemented
1006C3#1059404611yescharacteristic, complemented
1007C3#1059440811yescharacteristic, complemented
1008C2—62no—
1009C2—1081no—
1010C2D3×#379811yescharacteristic
1011C2#1172439311yescharacteristic
1012C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6291C22
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
1. #11723679C2semidirect
3. #11723452C2semidirect
4. #11723442C2semidirect
5. C3×#63878C2semidirect
6. C3×#63877C2semidirect
7. C3×#63867C2semidirect
8. #11723021C2semidirect
9. #11723021C2semidirect
10. #11723016C2semidirect
13. #11722980C2semidirect
14. #11722942C2semidirect
15. D3×#3724C2semidirect
75. #63878D3semidirect
76. #63877D3semidirect
90. #63867D3semidirect
661. C33#552semidirect
925. C32#5531semidirect
926. C32#5531semidirect
927. C32#5693semidirect
1005. C3#10593918semidirect
1006. C3#10594046semidirect
1007. C3#10594408semidirect

Maximal subgroups

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

subgroupindex
#117236792
#117234622
#117234522
#117234422
C3×#638782
C3×#638772
C3×#638672
#117230212
#117230162
#117229872
#117229802
#117229422
D3×#37242
#105944083
#105940463
#105939183