Finite Group Databasebeta

← #13168182

Subgroups — #13168182

Order 1728.

1102 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723683C211yesmaximal, characteristic, complemented
2#11723493C211yesmaximal, characteristic
3#11723477C211yesmaximal, characteristic, complemented
4#11723446C211yesmaximal, characteristic, complemented
5C3×#63888C211yesmaximal, characteristic, complemented
6C3×#63846C211yesmaximal, characteristic, complemented
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723021C211yesmaximal, characteristic, complemented
9#11723017C211yesmaximal, characteristic, complemented
10#11723012C211yesmaximal, characteristic, complemented
11#11722999C211yesmaximal, characteristic
12#11722933C211yesmaximal, characteristic
13#11722920C211yesmaximal, characteristic, complemented
14#11722919C211yesmaximal, characteristic, complemented
15#11722908C211yesmaximal, characteristic, complemented
16#10595379—31nomaximal
17#10594449—31nomaximal
18#10594349—31nomaximal
19C2×C32×Dic6C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6292C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25#88859C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88814C2211yescharacteristic
33#88813C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64155—31no—
55#64107—31no—
56#64103—31no—
57C3×#946—31no—
58C3×Q8×Dic3—31no—
59C3×#896—31no—
60C3×#890—31no—
61C3×#889—31no—
62C3×#887—31no—
63#63904—31no—
64C4×#626—31no—
65#63897—31no—
66#63894—31no—
67#63890—31no—
68#63890—31no—
69#63890—31no—
70#63890—31no—
71#63890—61no—
72D3×C4⋊Dic3—31no—
73D3×C4⋊Dic3—31no—
74#63888—31no—
75#63888—31no—
76#63888—61no—
77#63888D311yescharacteristic, complemented
78#63883—31no—
79#63878—31no—
80#63877—31no—
81#63877—31no—
82#63877—31no—
83#63874—31no—
84#63869—31no—
85#63868—31no—
86#63868—31no—
87#63868—31no—
88#63868—31no—
89#63868—61no—
90#63867—31no—
91#63849—31no—
92#63848—31no—
93#63847—31no—
94#63846—31no—
95#63846—31no—
96#63846D311yescharacteristic, complemented
97#63845—31no—
98#63843D311yescharacteristic, complemented
99#63836—31no—
100#63836—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×Dic6—22no—
118#6294—22no—
119#6292—22no—
120#6289—22no—
121Dic3×C3⋊D3—22no—
122C3×#624—22no—
123#5693—91no—
124#5642—91no—
125#5581—91no—
126C2×C32×Q8—31no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×Dic6—21no—
133C2×C3×Dic6C2×D311yescharacteristic
134C2×C3×Dic6C2×D311yescharacteristic
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—61no—
138C2×#624—31no—
139C2×#624—31no—
140C2×#624—31no—
141C2×#624—61no—
142C2×#624C2×D311yescharacteristic
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—61no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150#3752—31no—
151#3752—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—61no—
158#3752—61no—
159#3752—61no—
160#3752—121no—
161#3752C2×D311yescharacteristic
162C4⋊(C3⋊Dic3)—31no—
163C4⋊(C3⋊Dic3)—31no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750C2×D311yescharacteristic
168C4×C3⋊Dic3C2×D311yescharacteristic
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—61no—
174C3×C4⋊Dic3—21no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3C2×D311yescharacteristic
182C3×C4⋊Dic3C2×D311yescharacteristic
183C3×Dic3⋊C4—21no—
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—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—61no—
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—61no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—61no—
212#3724—61no—
213#3724C2×D311yescharacteristic
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
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—61no—
241#3722—61no—
242#3722—61no—
243#3722—61no—
244#3722C2×D311yescharacteristic
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32C2×D311yescharacteristic
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3⋊(C3⋊D3)—21no—
255C2×C3⋊(C3⋊D3)—21no—
256C2×C3⋊(C3⋊D3)—21no—
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3#4112yes—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×#125—91no—
274C3×C22⋊Q8—91no—
275C3×C4×Q8—91no—
276#946—31no—
277#946—91no—
278#946—91no—
279#946—181no—
280Q8×Dic3—31no—
281C4×#67—91no—
282C2×C4⋊Dic3—91no—
283#898—91no—
284#898—91no—
285#898—91no—
286#898—91no—
287#898—181no—
288#896—31no—
289#896—91no—
290#894—91no—
291#894—91no—
292#894—91no—
293#894—91no—
294#894—181no—
295#893—91no—
296#892—91no—
297#892—91no—
298#892—91no—
299D3×C4⋊C4—91no—
300D3×C4⋊C4—91no—
301#890—31no—
302#890—91no—
303#890—91no—
304#889—31no—
305#889—91no—
306#889—91no—
307#889—91no—
308#887—31no—
309#886—91no—
310#886—91no—
311#877—91no—
312#877—91no—
313#876—91no—
314#876—91no—
315C4×D12—91no—
316#872—91no—
317#872—91no—
318#872—91no—
319#872—91no—
320#870—91no—
321C22×C3⋊D3—31no—
322C22×C3⋊D3—31no—
323C22×C3⋊D3—31no—
324C22×C3⋊D3—61no—
325C22×C3⋊D3—61no—
326C22×C3⋊D3—61no—
327C22×C3⋊D3—121no—
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—61no—
332C32×Q8—62no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—21no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—41no—
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C32×C4C22×D311yescharacteristic
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—31no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—121no—
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C4⋊(C3⋊D3)—62no—
359C4×C3⋊D3—62no—
360C4×C3⋊D3—62no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C3×C4×D3—62no—
395C3×C4×D3—62no—
396C3×Dic6—22no—
397C3×Dic6—22no—
398C3×Dic6—42no—
399#626—62no—
400#626—62no—
401#626—122no—
402#624—22no—
403#624—62no—
404#624—62no—
405#624—62no—
406#624—122no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411D3×Dic3—122no—
412#552—271noSylow
413C2×C33C2×#4111yescharacteristic
414C2×C33C2×#4111yescharacteristic
415C2×C332−1+411yescharacteristic
416C3⋊(C3⋊D3)—41no—
417C3×C3⋊D3—22no—
418C2×C3×Q8—31no—
419C2×C3×Q8—31no—
420C2×C3×Q8—61no—
421C22×C3×C4—91no—
422C2×#67—91no—
423C22×Dic3—91no—
424C22×Dic3—91no—
425C2×D12—91no—
426C2×D12—91no—
427C2×D12—181no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—181no—
438C2×C4×D3—181no—
439C2×Dic6D3211yescharacteristic
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—61no—
445C3×C4⋊C4—61no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C42—91no—
457C3×C42—91no—
458C3×C42—91no—
459C3×C42—91no—
460#217—91no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—61no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—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—181no—
484(C2×D3)⋊C4—181no—
485(C2×D3)⋊C4—181no—
486(C2×D3)⋊C4—181no—
487(C2×D3)⋊C4—181no—
488(C2×D3)⋊C4—181no—
489(C2×D3)⋊C4—181no—
490(C2×D3)⋊C4—361no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—91no—
498C4⋊Dic3—91no—
499C4⋊Dic3—91no—
500C4⋊Dic3—91no—
501C4⋊Dic3—91no—
502C4⋊Dic3—91no—
503C4⋊Dic3—181no—
504C4⋊Dic3—181no—
505C4⋊Dic3D3211yescharacteristic
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—61no—
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—181no—
530Dic3⋊C4—181no—
531Dic3⋊C4—181no—
532Dic3⋊C4D3211yescharacteristic
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—31no—
541C4×Dic3—61no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—41no—
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C22×C32C23×D311yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—61no—
555C2×C3⋊D3—62no—
556C2×C3⋊D3—61no—
557C2×C3⋊D3—61no—
558C2×C3⋊D3—61no—
559C2×C3⋊D3—61no—
560C2×C3⋊D3—61no—
561C2×C3⋊D3—61no—
562C2×C3⋊D3—61no—
563C2×C3⋊D3—61no—
564C2×C3⋊D3—121no—
565C2×C3⋊D3—121no—
566C2×C3⋊D3—122no—
567C2×C3⋊D3—121no—
568C2×C3⋊D3—121no—
569C2×C3⋊D3—121no—
570C2×C3⋊D3—121no—
571C2×C3⋊D3—121no—
572C2×C3⋊D3—121no—
573C2×C3⋊D3—241no—
574C2×C3⋊D3—241no—
575C2×C3⋊D3#23912yes—
576C2×C3×D3—32no—
577C2×C3×D3—32no—
578C2×C3×D3—62no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—121no—
584C2×C3×D3—121no—
585C32×C4—21no—
586C32×C4—21no—
587C32×C4—21no—
588C32×C4—32no—
589C32×C4—41no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—61no—
593C32×C4—61no—
594C32×C4—61no—
595C32×C4—61no—
596C32×C4—61no—
597C32×C4—81no—
598C3⋊Dic3—21no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—61no—
604C3⋊Dic3—61no—
605C3⋊Dic3—61no—
606C3⋊Dic3—121no—
607C3⋊Dic3—121no—
608C3⋊Dic3—121no—
609C3⋊Dic3—241no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—22no—
621C3×Dic3—41no—
622C3×Dic3—41no—
623C3×Dic3—41no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—121no—
637C3×Dic3—121no—
638C3×Dic3—121no—
639C3×Dic3—121no—
640C3×Dic3—121no—
641C3×Dic3#23512yes—
642C3×Dic3#23712yes—
643#126—271no—
644#126—271no—
645#125—91no—
646#125—271no—
647#125—271no—
648#123—271no—
649#123—271no—
650C22⋊Q8—91no—
651C22⋊Q8—271no—
652C4×Q8—91no—
653C4×D4—271no—
654#117—271no—
655#117—271no—
656#117—271no—
657C2×C4⋊C4—271no—
658C33#55211yescharacteristic, complemented, Sylow
659C23×C3—91no—
660C22×D3—31no—
661C22×D3—31no—
662C22×D3—61no—
663C22×D3—91no—
664C22×D3—91no—
665C22×D3—91no—
666C22×D3—181no—
667C22×D3—181no—
668C22×D3—181no—
669C22×D3—361no—
670C3×Q8—62no—
671C3×Q8—62no—
672C3×Q8—122no—
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—31no—
687C2×C3×C4—31no—
688C2×C3×C4—41no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—91no—
699C2×C3×C4—91no—
700C2×C3×C4—182no—
701C2×C3×C4C2×D3211yescharacteristic
702C2×C3×C4C2×D3211yescharacteristic
703C2×C3×C4C2×D3211yescharacteristic
704#67—182no—
705C2×Dic3—31no—
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—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—91no—
721C2×Dic3—91no—
722C2×Dic3—91no—
723C2×Dic3—181no—
724C2×Dic3—181no—
725C2×Dic3—181no—
726C2×Dic3—182no—
727C2×Dic3—182no—
728C2×Dic3—361no—
729C2×Dic3C2×D3211yescharacteristic
730C2×Dic3C2×D3211yescharacteristic
731C2×Dic3C2×D3211yescharacteristic
732C2×Dic3C2×D3211yescharacteristic
733C2×Dic3C2×D3211yescharacteristic
734C2×Dic3C2×D3211yescharacteristic
735D12—182no—
736D12—182no—
737D12—362no—
738C4×D3—62no—
739C4×D3—62no—
740C4×D3—182no—
741C4×D3—182no—
742C4×D3—182no—
743C4×D3—182no—
744C4×D3—182no—
745C4×D3—182no—
746C4×D3—182no—
747C4×D3—362no—
748C4×D3—362no—
749Dic6—22no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—41no—
762C2×C32C2×#23511yescharacteristic
763C2×C32C2×#23711yescharacteristic
764C2×C32C2×#23911yescharacteristic
765C2×C32#100711yescharacteristic
766C2×C32#100711yescharacteristic
767C2×C32D3×#4111yescharacteristic
768C2×C32D3×#4111yescharacteristic
769C2×C32D3×#4111yescharacteristic
770C2×C32#101011yescharacteristic
771C3⋊D3—22no—
772C3⋊D3—121no—
773C3⋊D3—122no—
774C3⋊D3—121no—
775C3⋊D3—121no—
776C3⋊D3—241no—
777C3⋊D3—241no—
778C3⋊D3—242no—
779C3×D3—62no—
780C3×D3—62no—
781C3×D3—122no—
782C2×Q8—31no—
783C2×D4—271no—
784C22×C4—91no—
785C22×C4—271no—
786C22×C4—271no—
787C22×C4—271no—
788C4⋊C4—31no—
789C4⋊C4—31no—
790C4⋊C4—91no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4—91no—
794C4⋊C4—91no—
795C4⋊C4—91no—
796C4⋊C4—91no—
797C4⋊C4—91no—
798C4⋊C4—271no—
799C4⋊C4—271no—
800C4⋊C4—271no—
801C4⋊C4—271no—
802C4⋊C4—271no—
803C4⋊C4—271no—
804C22⋊C4—91no—
805C22⋊C4—91no—
806C22⋊C4—271no—
807C22⋊C4—271no—
808C22⋊C4—271no—
809C22⋊C4—271no—
810C22⋊C4—271no—
811C22⋊C4—271no—
812C42—91no—
813C42—91no—
814C42—91no—
815C42—91no—
816C42—271no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—41no—
821C22×C3—92no—
822C22×C3—181no—
823C22×C3—181no—
824C22×C3C22×D3211yescharacteristic
825C22×C3C22×D3211yescharacteristic
826C22×C3C22×D3211yescharacteristic
827C2×D3—32no—
828C2×D3—32no—
829C2×D3—62no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—182no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—181no—
844C2×D3—181no—
845C2×D3—181no—
846C2×D3—361no—
847C2×D3—361no—
848C2×D3—361no—
849C2×D3—361no—
850C2×D3—361no—
851C2×D3—361no—
852C2×D3—361no—
853C2×D3—361no—
854C2×D3—362no—
855C2×D3—721no—
856C2×D3—721no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—32no—
861C3×C4—32no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—62no—
866C3×C4—61no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—61no—
870C3×C4—61no—
871C3×C4—61no—
872C3×C4—61no—
873C3×C4—61no—
874C3×C4—61no—
875C3×C4—61no—
876C3×C4—81no—
877C3×C4—121no—
878C3×C4—121no—
879C3×C4—121no—
880C3×C4—121no—
881C3×C4—121no—
882C3×C4—181no—
883C3×C4—181no—
884C3×C4—181no—
885C3×C4—181no—
886C3×C4—181no—
887Dic3—21no—
888Dic3—21no—
889Dic3—21no—
890Dic3—21no—
891Dic3—21no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—61no—
901Dic3—61no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—121no—
907Dic3—181no—
908Dic3—181no—
909Dic3—181no—
910Dic3—361no—
911Dic3—361no—
912Dic3—361no—
913Dic3—721no—
914Dic3#380412yes—
915C32—21no—
916C32—21no—
917C32—21no—
918C32—41no—
919C32#558111yescharacteristic, complemented
920C32#564211yescharacteristic, complemented
921C32#569311yescharacteristic, complemented
922C23—91no—
923C23—271no—
924Q8—62no—
925D4—542no—
926C2×C4—31no—
927C2×C4—31no—
928C2×C4—31no—
929C2×C4—31no—
930C2×C4—31no—
931C2×C4—31no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—182no—
938C2×C4—271no—
939C2×C4—542no—
940C2×C4—542no—
941C2×C4—542no—
942C2×C4D3311yescharacteristic
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—41no—
953C2×C3—41no—
954C2×C3—41no—
955C2×C3—182no—
956C2×C3#6429711yescharacteristic
957C2×C3D3×#23511yescharacteristic
958C2×C3D3×#23711yescharacteristic
959C2×C3#6431211yescharacteristic
960C2×C3#6431511yescharacteristic
961C2×C3#6431611yescharacteristic
962C2×C3D3×#23911yescharacteristic
963C2×C3D3×#23911yescharacteristic
964C2×C3C2×#380411yescharacteristic
965D3—62no—
966D3—62no—
967D3—122no—
968D3—362no—
969D3—361no—
970D3—361no—
971D3—361no—
972D3—721no—
973D3—721no—
974D3—722no—
975C22—92no—
976C22—181no—
977C22—181no—
978C22—541no—
979C22—541no—
980C22—541no—
981C22C2×D3311yescharacteristic
982C4—21no—
983C4—32no—
984C4—61no—
985C4—61no—
986C4—61no—
987C4—61no—
988C4—61no—
989C4—181no—
990C4—181no—
991C4—181no—
992C4—181no—
993C4—181no—
994C4—541no—
995C3—21no—
996C3—21no—
997C3—21no—
998C3—41no—
999C3#1059434911yescharacteristic, complemented
1000C3#1059444911yescharacteristic, complemented
1001C3#1059537911yescharacteristic, complemented
1002C2—182no—
1003C2—1081no—
1004C2#1172437711yescharacteristic
1005C2#1172439711yescharacteristic
1006C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6292C22
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. #11723683C2semidirect
3. #11723477C2semidirect
4. #11723446C2semidirect
5. C3×#63888C2semidirect
6. C3×#63846C2semidirect
7. C3×#63843C2semidirect
8. #11723021C2semidirect
9. #11723017C2semidirect
10. #11723012C2semidirect
13. #11722920C2semidirect
14. #11722919C2semidirect
15. #11722908C2semidirect
77. #63888D3semidirect
96. #63846D3semidirect
98. #63843D3semidirect
658. C33#552semidirect
919. C32#5581semidirect
920. C32#5642semidirect
921. C32#5693semidirect
999. C3#10594349semidirect
1000. C3#10594449semidirect
1001. C3#10595379semidirect

Maximal subgroups

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

subgroupindex
#117236832
#117234932
#117234772
#117234462
C3×#638882
C3×#638462
C3×#638432
#117230212
#117230172
#117230122
#117229992
#117229332
#117229202
#117229192
#117229082
#105953793
#105944493
#105943493