Finite Group Databasebeta

← #13168265

Subgroups — #13168265

Order 1728.

1134 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#11723691C211yesmaximal, characteristic, complemented
2#11723485C211yesmaximal, characteristic, complemented
3#11723482C211yesmaximal, characteristic
4#11723446C211yesmaximal, characteristic, complemented
5C3×#63897C211yesmaximal, characteristic, complemented
6C3×#63870C211yesmaximal, characteristic, complemented
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723000C211yesmaximal, characteristic, complemented
10#11722999C211yesmaximal, characteristic, complemented
11#11722993C211yesmaximal, characteristic, complemented
12#11722984C211yesmaximal, characteristic, complemented
13#11722983C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722908C211yesmaximal, characteristic, complemented
16#10594483—31nomaximal
17#10594443—31nomaximal
18#10594440—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28#88859C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×C4×C3⋊Dic3C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88803C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64107—31no—
55#64106—31no—
56#64104—31no—
57C3×#894—31no—
58C3×#894—31no—
59C3×#890—31no—
60C3×#889—31no—
61C3×#889—31no—
62C3×#889—31no—
63#63899—31no—
64#63898—31no—
65#63897—31no—
66#63897—31no—
67#63897—31no—
68#63897D311yescharacteristic, complemented
69#63896—31no—
70#63896—31no—
71#63895—31no—
72#63895—31no—
73#63895—31no—
74#63895—61no—
75#63894—31no—
76#63894—31no—
77#63893—31no—
78Dic3×D12—31no—
79#63890—31no—
80#63890—31no—
81D3×C4⋊Dic3—31no—
82D3×C4⋊Dic3—31no—
83#63886—31no—
84#63886—31no—
85#63886—61no—
86#63883—31no—
87#63881—31no—
88#63880—31no—
89#63870D311yescharacteristic, complemented
90#63868—31no—
91#63868—31no—
92#63868—31no—
93#63868—61no—
94#63865—31no—
95#63861—31no—
96#63859—31no—
97#63854—31no—
98#63853—31no—
99#63850—31no—
100#63850—31no—
101#63845D311yescharacteristic, complemented
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊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
111C3×C4⋊(C3⋊D3)—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6294—41no—
119#6294—41no—
120#6293—41no—
121#6292—22no—
122#6292—41no—
123#6289—41no—
124Dic3×C3⋊D3—41no—
125C3×#624—22no—
126#5692—91no—
127#5692—91no—
128#5665—91no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×#634—31no—
135C2×C3×D12—31no—
136C2×C3×D12—31no—
137C2×C3×D12—61no—
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—31no—
146C2×#626—31no—
147C2×#626—61no—
148C2×#626—61no—
149C2×#624—31no—
150C2×#624—31no—
151C2×#624—31no—
152C2×#624—31no—
153C2×#624—61no—
154C2×#624C2×D311yescharacteristic
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—61no—
162C32×C4⋊C4—31no—
163C32×C4⋊C4—31no—
164C32×C4⋊C4—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—61no—
173#3752—61no—
174#3752—61no—
175#3752—121no—
176C4⋊(C3⋊Dic3)—31no—
177C4⋊(C3⋊Dic3)—31no—
178C4⋊(C3⋊Dic3)C2×D311yescharacteristic
179#3750—31no—
180C4×C3⋊Dic3C2×D311yescharacteristic
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—31no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—61no—
194C3×Dic3⋊C4—21no—
195C3×Dic3⋊C4—21no—
196C3×Dic3⋊C4—21no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4C2×D311yescharacteristic
208C3×Dic3⋊C4C2×D311yescharacteristic
209C3×Dic3⋊C4C2×D311yescharacteristic
210C3×Dic3⋊C4C2×D311yescharacteristic
211C3×Dic3⋊C4C2×D311yescharacteristic
212C3×Dic3⋊C4C2×D311yescharacteristic
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—61no—
218#3724—31no—
219#3724—31no—
220#3724—61no—
221#3724C2×D311yescharacteristic
222#3724C2×D311yescharacteristic
223#3724C2×D311yescharacteristic
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234#3722—31no—
235#3722—31no—
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#3722C2×D311yescharacteristic
246#3722C2×D311yescharacteristic
247#3722C2×D311yescharacteristic
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—61no—
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊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—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#125—91no—
279C3×#125—91no—
280C3×#123—91no—
281#939—91no—
282D4×Dic3—91no—
283#929—91no—
284C2×C4⋊Dic3—91no—
285#898—91no—
286#898—91no—
287#898—91no—
288#898—181no—
289#897—91no—
290#897—91no—
291#897—91no—
292#897—181no—
293#896—91no—
294#896—91no—
295#896—91no—
296#896—91no—
297#895—91no—
298#895—91no—
299#895—181no—
300#894—31no—
301#894—31no—
302#894—91no—
303#894—91no—
304#894—91no—
305#894—91no—
306#894—91no—
307#894—91no—
308#893—91no—
309#893—91no—
310D3×C4⋊C4—91no—
311D3×C4⋊C4—91no—
312#890—31no—
313#889—31no—
314#889—31no—
315#889—31no—
316#886—91no—
317#883—91no—
318#67⋊C4—91no—
319#879—91no—
320#878—91no—
321#878—91no—
322#876—91no—
323#876—91no—
324C4×D12—91no—
325C4×D12—91no—
326C22×C3⋊D3—31no—
327C22×C3⋊D3—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—61no—
330C22×C3⋊D3—61no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—121no—
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—31no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—61no—
340C22×C3×D3—61no—
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—31no—
349C2×C32×C4—31no—
350C2×C32×C4—41no—
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353C2×C32×C4C22×D311yescharacteristic
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—121no—
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C4⋊(C3⋊D3)—22no—
366C4⋊(C3⋊D3)—62no—
367C4⋊(C3⋊D3)—121no—
368C4×C3⋊D3—121no—
369C4×C3⋊D3—121no—
370#634—121no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
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—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
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
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C3×D12—62no—
402C3×D12—62no—
403C3×D12—122no—
404C3×C4×D3—62no—
405C3×C4×D3—62no—
406#627—121no—
407#627—121no—
408#627—122no—
409#626—62no—
410#626—62no—
411#626—122no—
412#626—121no—
413#626—121no—
414#626—122no—
415#624—22no—
416#624—121no—
417#624—121no—
418#624—122no—
419#624—121no—
420#624—121no—
421D3×Dic3—121no—
422D3×Dic3—121no—
423D3×Dic3—122no—
424D3×Dic3—121no—
425D3×Dic3—121no—
426D3×Dic3—121no—
427D3×Dic3—121no—
428#539—271noSylow
429C2×C33C2×#4111yescharacteristic
430C2×C33H(5,𝔽2)11yescharacteristic
431C2×C332−1+411yescharacteristic
432C3⋊(C3⋊D3)—41no—
433C3×C3⋊D3—22no—
434C3×C3⋊D3—41no—
435C2×C3×D4—91no—
436C22×C3×C4—91no—
437C2×#67—91no—
438C2×#67—91no—
439C22×Dic3—91no—
440C22×Dic3—91no—
441C22×Dic3—91no—
442C2×D12—31no—
443C2×D12—31no—
444C2×D12—61no—
445C2×D12—91no—
446C2×D12—91no—
447C2×D12—91no—
448C2×D12—91no—
449C2×D12—181no—
450C2×D12—181no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—91no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—181no—
463C2×C4×D3—181no—
464C2×Dic6—91no—
465C2×Dic6—91no—
466C2×Dic6—91no—
467C2×Dic6—181no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—61no—
475C3×C4⋊C4—61no—
476C3×C4⋊C4—61no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C22⋊C4—91no—
486C3×C22⋊C4—91no—
487C3×C22⋊C4—91no—
488C3×C42—91no—
489C3×C42—91no—
490#217—91no—
491#217—91no—
492#217—91no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
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—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—91no—
514(C2×D3)⋊C4—91no—
515(C2×D3)⋊C4—91no—
516(C2×D3)⋊C4—91no—
517(C2×D3)⋊C4—181no—
518(C2×D3)⋊C4—181no—
519(C2×D3)⋊C4—181no—
520(C2×D3)⋊C4—181no—
521(C2×D3)⋊C4—181no—
522(C2×D3)⋊C4—181no—
523(C2×D3)⋊C4—181no—
524(C2×D3)⋊C4—361no—
525C4⋊Dic3—31no—
526C4⋊Dic3—31no—
527C4⋊Dic3—31no—
528C4⋊Dic3—31no—
529C4⋊Dic3—31no—
530C4⋊Dic3—31no—
531C4⋊Dic3—61no—
532C4⋊Dic3—91no—
533C4⋊Dic3—91no—
534C4⋊Dic3—91no—
535C4⋊Dic3—91no—
536C4⋊Dic3—181no—
537C4⋊Dic3—181no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—31no—
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—31no—
545Dic3⋊C4—31no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—181no—
554Dic3⋊C4D3211yescharacteristic
555Dic3⋊C4D3211yescharacteristic
556Dic3⋊C4D3211yescharacteristic
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—31no—
560C4×Dic3—31no—
561C4×Dic3—61no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—41no—
566C22×C32C23×D311yescharacteristic
567C22×C32C23×D311yescharacteristic
568C22×C32C23×D311yescharacteristic
569C2×C3⋊D3—21no—
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—61no—
575C2×C3⋊D3—62no—
576C2×C3⋊D3—61no—
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—121no—
585C2×C3⋊D3—121no—
586C2×C3⋊D3—122no—
587C2×C3⋊D3—121no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—241no—
594C2×C3⋊D3—241no—
595C2×C3⋊D3#23712yes—
596C2×C3×D3—32no—
597C2×C3×D3—32no—
598C2×C3×D3—62no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—121no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
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—61no—
625C32×C4—61no—
626C32×C4—81no—
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—22no—
639C3×Dic3—22no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—21no—
650C3×Dic3—21no—
651C3×Dic3—21no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—41no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—121no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668#126—271no—
669#126—271no—
670#125—91no—
671#125—91no—
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—271no—
683C33#53911yescharacteristic, complemented, Sylow
684C23×C3—91no—
685C23×C3—91no—
686C22×D3—31no—
687C22×D3—31no—
688C22×D3—31no—
689C22×D3—31no—
690C22×D3—61no—
691C22×D3—61no—
692C22×D3—91no—
693C22×D3—91no—
694C22×D3—91no—
695C22×D3—181no—
696C22×D3—181no—
697C22×D3—181no—
698C22×D3—361no—
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—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—41no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—91no—
725C2×C3×C4—91no—
726C2×C3×C4—182no—
727C2×C3×C4C2×D3211yescharacteristic
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730#67—182no—
731#67—361no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—91no—
747C2×Dic3—181no—
748C2×Dic3—181no—
749C2×Dic3—181no—
750C2×Dic3—361no—
751C2×Dic3—361no—
752C2×Dic3—361no—
753C2×Dic3—361no—
754C2×Dic3C2×D3211yescharacteristic
755C2×Dic3C2×D3211yescharacteristic
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758C2×Dic3C2×D3211yescharacteristic
759C2×Dic3C2×D3211yescharacteristic
760D12—62no—
761D12—62no—
762D12—122no—
763D12—182no—
764D12—182no—
765D12—362no—
766D12—361no—
767D12—361no—
768D12—362no—
769C4×D3—62no—
770C4×D3—62no—
771C4×D3—361no—
772C4×D3—361no—
773C4×D3—361no—
774C4×D3—361no—
775C4×D3—361no—
776C4×D3—361no—
777C4×D3—361no—
778C4×D3—362no—
779C4×D3—361no—
780C4×D3—361no—
781C4×D3—362no—
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×C32C2×#23711yescharacteristic
799C2×C32#100711yescharacteristic
800C2×C32#100711yescharacteristic
801C2×C32D3×#4111yescharacteristic
802C2×C32D3×#4111yescharacteristic
803C2×C32#100911yescharacteristic
804C2×C32#100911yescharacteristic
805C2×C32#100911yescharacteristic
806C2×C32#101011yescharacteristic
807C3⋊D3—22no—
808C3⋊D3—41no—
809C3⋊D3—121no—
810C3⋊D3—122no—
811C3⋊D3—121no—
812C3⋊D3—121no—
813C3⋊D3—241no—
814C3⋊D3—241no—
815C3⋊D3—242no—
816C3×D3—62no—
817C3×D3—62no—
818C3×D3—122no—
819C3×D3—121no—
820C3×D3—121no—
821C3×D3—241no—
822C2×Q8—271no—
823C2×D4—91no—
824C2×D4—271no—
825C2×D4—271no—
826C22×C4—91no—
827C22×C4—271no—
828C22×C4—271no—
829C22×C4—271no—
830C22×C4—271no—
831C4⋊C4—31no—
832C4⋊C4—31no—
833C4⋊C4—31no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—91no—
841C4⋊C4—91no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—91no—
848C22⋊C4—271no—
849C22⋊C4—271no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C42—91no—
856C42—91no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—41no—
861C22×C3—92no—
862C22×C3—181no—
863C22×C3—181no—
864C22×C3—181no—
865C22×C3—181no—
866C22×C3—181no—
867C22×C3C22×D3211yescharacteristic
868C22×C3C22×D3211yescharacteristic
869C22×C3C22×D3211yescharacteristic
870C2×D3—32no—
871C2×D3—32no—
872C2×D3—62no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—61no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—182no—
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—181no—
898C2×D3—361no—
899C2×D3—361no—
900C2×D3—361no—
901C2×D3—361no—
902C2×D3—361no—
903C2×D3—361no—
904C2×D3—361no—
905C2×D3—361no—
906C2×D3—362no—
907C2×D3—721no—
908C2×D3—721no—
909C3×C4—21no—
910C3×C4—21no—
911C3×C4—21no—
912C3×C4—41no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—62no—
916C3×C4—62no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—61no—
925C3×C4—61no—
926C3×C4—61no—
927C3×C4—61no—
928C3×C4—61no—
929C3×C4—81no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—121no—
933C3×C4—121no—
934C3×C4—181no—
935C3×C4—181no—
936C3×C4—181no—
937C3×C4—181no—
938Dic3—21no—
939Dic3—21no—
940Dic3—21no—
941Dic3—21no—
942Dic3—21no—
943Dic3—21no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
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#566511yescharacteristic, complemented
968C32#569211yescharacteristic, complemented
969C32#569211yescharacteristic, complemented
970C23—91no—
971C23—91no—
972C23—271no—
973Q8—1081no—
974D4—182no—
975D4—542no—
976D4—1081no—
977C2×C4—31no—
978C2×C4—31no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—182no—
988C2×C4—271no—
989C2×C4—1081no—
990C2×C4—1081no—
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—182no—
1007C2×C3—361no—
1008C2×C3#6429711yescharacteristic
1009C2×C3#6430811yescharacteristic
1010C2×C3#6430811yescharacteristic
1011C2×C3D3×#23711yescharacteristic
1012C2×C3D3×#23711yescharacteristic
1013C2×C3#6431211yescharacteristic
1014C2×C3#6431511yescharacteristic
1015C2×C3#6431611yescharacteristic
1016C2×C3#6432011yescharacteristic
1017D3—62no—
1018D3—62no—
1019D3—122no—
1020D3—121no—
1021D3—121no—
1022D3—241no—
1023D3—362no—
1024D3—361no—
1025D3—361no—
1026D3—361no—
1027D3—721no—
1028D3—721no—
1029D3—722no—
1030C22—92no—
1031C22—181no—
1032C22—181no—
1033C22—181no—
1034C22—181no—
1035C22—181no—
1036C22—541no—
1037C22—541no—
1038C22—541no—
1039C22C2×D3311yescharacteristic
1040C4—21no—
1041C4—61no—
1042C4—61no—
1043C4—61no—
1044C4—61no—
1045C4—61no—
1046C4—61no—
1047C4—181no—
1048C4—181no—
1049C4—181no—
1050C4—181no—
1051C4—541no—
1052C3—21no—
1053C3—21no—
1054C3—21no—
1055C3—41no—
1056C3#1059444011yescharacteristic, complemented
1057C3#1059444311yescharacteristic, complemented
1058C3#1059448311yescharacteristic, complemented
1059C2—182no—
1060C2—361no—
1061C2—1081no—
1062C2#1172439011yescharacteristic
1063C2#1172439711yescharacteristic
1064C2#1172440811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723482C2
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. #11723691C2semidirect
2. #11723485C2semidirect
4. #11723446C2semidirect
5. C3×#63897C2semidirect
6. C3×#63870C2semidirect
7. C3×#63845C2semidirect
8. #11723023C2semidirect
9. #11723000C2semidirect
10. #11722999C2semidirect
11. #11722993C2semidirect
12. #11722984C2semidirect
13. #11722983C2semidirect
14. #11722937C2semidirect
15. #11722908C2semidirect
68. #63897D3semidirect
89. #63870D3semidirect
101. #63845D3semidirect
683. C33#539semidirect
967. C32#5665semidirect
968. C32#5692semidirect
969. C32#5692semidirect
1056. C3#10594440semidirect
1057. C3#10594443semidirect
1058. C3#10594483semidirect

Maximal subgroups

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

subgroupindex
#117236912
#117234852
#117234822
#117234462
C3×#638972
C3×#638702
C3×#638452
#117230232
#117230002
#117229992
#117229932
#117229842
#117229832
#117229372
#117229082
#105944833
#105944433
#105944403