Finite Group Databasebeta

← #13168237

Subgroups — #13168237

Order 1728.

1160 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723684C211yesmaximal, characteristic
2#11723476C211yesmaximal, characteristic, complemented
3C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#11723412C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic, complemented
6C3×#63871C211yesmaximal, characteristic, complemented
7C3×#63839C211yesmaximal, characteristic, complemented
8#11723017C211yesmaximal, characteristic, complemented
9#11722979C211yesmaximal, characteristic, complemented
10#11722974C211yesmaximal, characteristic, complemented
11#11722974C211yesmaximal, characteristic, complemented
12#11722940C211yesmaximal, characteristic, complemented
13#11722938C211yesmaximal, characteristic
14#11722934C211yesmaximal, characteristic
15#11722908C211yesmaximal, characteristic, complemented
16#10595372—31nomaximal
17#10594535—31nomaximal
18#10594393—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29#88857C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic
34#88814C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64155—31no—
55C4⋊C4×C3⋊D3—31no—
56#64098—31no—
57C3×#946—31no—
58C3×#944—31no—
59C3×#897—31no—
60C3×#897—31no—
61C3×#896—31no—
62C3×#888—31no—
63#63904—31no—
64C4×#626—31no—
65#63902—31no—
66#63899—31no—
67#63895D311yescharacteristic, complemented
68#63893—31no—
69#63893—31no—
70D3×C4⋊Dic3—31no—
71D3×C4⋊Dic3—31no—
72#63888—31no—
73#63887—31no—
74#63887—31no—
75#63887—31no—
76#63887—31no—
77#63887—31no—
78#63887—61no—
79#63883—31no—
80#63881—31no—
81#63881—31no—
82#63881—31no—
83#63880—31no—
84#63879—31no—
85#63879—31no—
86D3×Dic3⋊C4—31no—
87D3×Dic3⋊C4—31no—
88D3×Dic3⋊C4—61no—
89#63871—31no—
90#63871—31no—
91#63871D311yescharacteristic, complemented
92#63847—31no—
93#63846—31no—
94#63846—31no—
95#63846—31no—
96#63846—61no—
97#63845—31no—
98#63843—31no—
99Dic3×Dic6—31no—
100#63839D311yescharacteristic, complemented
101#63837—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
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—41no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×Dic6—41no—
119#6295Q814yescomplemented
120#6294—41no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3—41no—
123Dic3×C3⋊D3—41no—
124C3×#627—22no—
125C3×#627—41no—
126C3×#624—22no—
127#5730—91no—
128#5636—91no—
129#5635—91no—
130C2×C32×Q8—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3C2×D311yescharacteristic
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—61no—
140C2×C3×Dic6—21no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—31no—
143C2×C3×Dic6—31no—
144C2×C3×Dic6—31no—
145C2×C3×Dic6C2×D311yescharacteristic
146C2×C3×Dic6C2×D311yescharacteristic
147C2×#627C2×D311yescharacteristic
148C2×#627C2×D311yescharacteristic
149C2×#626—31no—
150C2×#626—31no—
151C2×#625—31no—
152C2×#624—31no—
153C2×#624C2×D311yescharacteristic
154C2×D3×Dic3—31no—
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—31no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3—61no—
164C2×D3×Dic3—61no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4—31no—
167#3752—31no—
168#3752C2×D311yescharacteristic
169C4⋊(C3⋊Dic3)—31no—
170C4⋊(C3⋊Dic3)—31no—
171C4⋊(C3⋊Dic3)—31no—
172#3750—31no—
173#3750—31no—
174#3750—31no—
175#3750—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—61no—
180#3750—61no—
181#3750—61no—
182#3750—121no—
183#3750C2×D311yescharacteristic
184C4×C3⋊Dic3—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—61no—
194C3×C4⋊Dic3—21no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3C2×D311yescharacteristic
200C3×C4⋊Dic3C2×D311yescharacteristic
201C3×Dic3⋊C4—21no—
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⋊C4C2×D311yescharacteristic
212C3×Dic3⋊C4C2×D311yescharacteristic
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215#3724—31no—
216#3724—31no—
217#3724—61no—
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⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241#3722—31no—
242#3722C2×D311yescharacteristic
243#3722C2×D311yescharacteristic
244#3722C2×D311yescharacteristic
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32C2×D311yescharacteristic
257C22×C33C2411yescharacteristic
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3C2×Q812yes—
263C2×C3×C3⋊D3C2×Q812yes—
264C33×C4—21no—
265C3⋊(C3⋊Dic3)—21no—
266C3⋊(C3⋊Dic3)—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3C2×Q812yes—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3#4112yes—
277C3×C4⋊Q8—91no—
278C3×C22⋊Q8—91no—
279C3×C22⋊Q8—91no—
280#946—31no—
281#946—91no—
282#946—91no—
283#946—91no—
284#946—91no—
285#946—91no—
286#946—181no—
287Q8×Dic3—91no—
288#944—31no—
289C4×#67—91no—
290C4×#67—91no—
291C2×C4⋊Dic3—91no—
292C2×Dic3⋊C4—91no—
293#897—31no—
294#897—31no—
295#897—91no—
296#897—91no—
297#896—31no—
298#896—91no—
299#893—91no—
300#893—91no—
301D3×C4⋊C4—91no—
302D3×C4⋊C4—91no—
303D3×C4⋊C4—91no—
304D3×C4⋊C4—91no—
305D3×C4⋊C4—181no—
306#890—91no—
307#890—91no—
308#889—91no—
309#889—91no—
310#889—91no—
311#889—91no—
312#889—181no—
313#888—31no—
314#887—91no—
315#67⋊C4—91no—
316#67⋊C4—91no—
317#67⋊C4—91no—
318#67⋊C4—91no—
319#878—91no—
320#878—91no—
321#878—91no—
322#878—91no—
323C4×D12—91no—
324C4×Dic6—91no—
325C22×C3⋊D3C22×D311yescharacteristic
326C22×C3⋊D3C22×D311yescharacteristic
327C22×C3×D3—31no—
328C22×C3×D3—31no—
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—61no—
332C22×C3×D3—61no—
333C32×Q8—121no—
334C2×C32×C4—21no—
335C2×C32×C4—21no—
336C2×C32×C4—21no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—41no—
344C2×C32×C4C22×D311yescharacteristic
345C2×C32×C4C22×D311yescharacteristic
346C2×C32×C4C22×D311yescharacteristic
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—31no—
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—61no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—121no—
360C2×C3⋊Dic3—121no—
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C4×C3⋊D3—41no—
366C4×C3⋊D3—62no—
367C4×C3⋊D3—121no—
368C4×C3⋊D3—121no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
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—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
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
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C3×C4×D3—62no—
400C3×C4×D3—62no—
401C3×C4×D3—121no—
402C3×C4×D3—121no—
403C3×C4×D3—122no—
404C3×Dic6—41no—
405C3×Dic6—41no—
406C3×Dic6—42no—
407C3×Dic6—62no—
408C3×Dic6—62no—
409C3×Dic6—121no—
410C3×Dic6—121no—
411#627—22no—
412#627—41no—
413#626—34no—
414#626—34no—
415#625—34no—
416#624—22no—
417#624—121no—
418D3×Dic3—64no—
419D3×Dic3—62no—
420D3×Dic3—62no—
421D3×Dic3—121no—
422D3×Dic3—121no—
423D3×Dic3—121no—
424D3×Dic3—121no—
425D3×Dic3—122no—
426D3×Dic3—122no—
427D3×Dic3—121no—
428D3×Dic3—121no—
429#554—271noSylow
430C2×C33C22×Q811yescharacteristic
431C2×C33C2×#4111yescharacteristic
432C2×C33H(5,𝔽2)11yescharacteristic
433C3×C3⋊D3—22no—
434C3×C3⋊D3—22no—
435C2×C3×Q8—31no—
436C2×C3×Q8—31no—
437C2×C3×Q8—61no—
438C2×C3×Q8—91no—
439C2×C3×Q8—91no—
440C22×C3×C4—91no—
441C22×C3×C4—91no—
442C2×#67—91no—
443C2×#67—91no—
444C22×Dic3—91no—
445C22×Dic3—91no—
446C22×Dic3—91no—
447C22×Dic3—91no—
448C2×D12—91no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—61no—
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×C4×D3—181no—
465C2×Dic6—31no—
466C2×Dic6—31no—
467C2×Dic6—31no—
468C2×Dic6—31no—
469C2×Dic6D3211yescharacteristic
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—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C22⋊C4—91no—
486C3×C42—91no—
487#217—91no—
488#217—91no—
489(C2×D3)⋊C4—31no—
490(C2×D3)⋊C4—31no—
491(C2×D3)⋊C4—31no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—61no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—181no—
503C4⋊Dic3—31no—
504C4⋊Dic3—31no—
505C4⋊Dic3—31no—
506C4⋊Dic3—31no—
507C4⋊Dic3—91no—
508C4⋊Dic3—91no—
509C4⋊Dic3—91no—
510C4⋊Dic3—91no—
511C4⋊Dic3—91no—
512C4⋊Dic3—91no—
513C4⋊Dic3—91no—
514C4⋊Dic3—91no—
515C4⋊Dic3—91no—
516C4⋊Dic3—181no—
517C4⋊Dic3—181no—
518C4⋊Dic3—181no—
519C4⋊Dic3D3211yescharacteristic
520Dic3⋊C4—31no—
521Dic3⋊C4—31no—
522Dic3⋊C4—31no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—61no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—181no—
545Dic3⋊C4—181no—
546Dic3⋊C4—181no—
547Dic3⋊C4—181no—
548Dic3⋊C4—181no—
549Dic3⋊C4—181no—
550Dic3⋊C4—181no—
551Dic3⋊C4—361no—
552Dic3⋊C4D3211yescharacteristic
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—181no—
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⋊D3D3×Q812yes—
574C2×C3⋊D3D3×Q812yes—
575C2×C3×D3—32no—
576C2×C3×D3—32no—
577C2×C3×D3—32no—
578C2×C3×D3—32no—
579C2×C3×D3—62no—
580C2×C3×D3—62no—
581C2×C3×D3—62no—
582C2×C3×D3—62no—
583C2×C3×D3—61no—
584C2×C3×D3—61no—
585C2×C3×D3—61no—
586C2×C3×D3—61no—
587C2×C3×D3—61no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—121no—
592C2×C3×D3—121no—
593C32×C4—21no—
594C32×C4—21no—
595C32×C4—21no—
596C32×C4—32no—
597C32×C4—41no—
598C32×C4—41no—
599C32×C4—41no—
600C32×C4—61no—
601C32×C4—61no—
602C32×C4—61no—
603C32×C4—61no—
604C32×C4—61no—
605C32×C4—81no—
606C3⋊Dic3—21no—
607C3⋊Dic3—21no—
608C3⋊Dic3—21no—
609C3⋊Dic3—61no—
610C3⋊Dic3—62no—
611C3⋊Dic3—61no—
612C3⋊Dic3—61no—
613C3⋊Dic3—61no—
614C3⋊Dic3—61no—
615C3⋊Dic3—61no—
616C3⋊Dic3—121no—
617C3⋊Dic3—121no—
618C3⋊Dic3—122no—
619C3⋊Dic3—121no—
620C3⋊Dic3—121no—
621C3⋊Dic3—121no—
622C3⋊Dic3—241no—
623C3⋊Dic3D3×Q812yes—
624C3×Dic3—22no—
625C3×Dic3—21no—
626C3×Dic3—21no—
627C3×Dic3—21no—
628C3×Dic3—21no—
629C3×Dic3—21no—
630C3×Dic3—21no—
631C3×Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—22no—
636C3×Dic3—32no—
637C3×Dic3—32no—
638C3×Dic3—41no—
639C3×Dic3—41no—
640C3×Dic3—41no—
641C3×Dic3—41no—
642C3×Dic3—62no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—121no—
650C3×Dic3—121no—
651C3×Dic3—121no—
652C3×Dic3#23712yes—
653C3×Dic3#23912yes—
654C4⋊Q8—91no—
655#125—271no—
656#125—271no—
657C22⋊Q8—91no—
658C22⋊Q8—91no—
659C22⋊Q8—271no—
660C22⋊Q8—271no—
661C22⋊Q8—271no—
662C22⋊Q8—271no—
663C4×Q8—271no—
664C4×D4—271no—
665C4×D4—271no—
666C4×D4—271no—
667C2×C4⋊C4—271no—
668C2×C4⋊C4—271no—
669C33#55411yescharacteristic, complemented, Sylow
670C23×C3—91no—
671C23×C3—91no—
672C22×D3—31no—
673C22×D3—31no—
674C22×D3—31no—
675C22×D3—31no—
676C22×D3—61no—
677C22×D3—61no—
678C3×Q8—121no—
679C3×Q8—121no—
680C3×Q8—122no—
681C3×Q8—182no—
682C3×Q8—361no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—31no—
687C2×C3×C4—31no—
688C2×C3×C4—31no—
689C2×C3×C4—31no—
690C2×C3×C4—31no—
691C2×C3×C4—31no—
692C2×C3×C4—31no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—41no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—91no—
706C2×C3×C4—91no—
707C2×C3×C4—91no—
708C2×C3×C4—91no—
709C2×C3×C4—182no—
710C2×C3×C4—361no—
711C2×C3×C4C2×D3211yescharacteristic
712C2×C3×C4C2×D3211yescharacteristic
713C2×C3×C4C2×D3211yescharacteristic
714#67—94no—
715#67—94no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—31no—
719C2×Dic3—31no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—31no—
723C2×Dic3—31no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—91no—
729C2×Dic3—91no—
730C2×Dic3—91no—
731C2×Dic3—91no—
732C2×Dic3—91no—
733C2×Dic3—91no—
734C2×Dic3—181no—
735C2×Dic3—181no—
736C2×Dic3—181no—
737C2×Dic3—181no—
738C2×Dic3—181no—
739C2×Dic3—181no—
740C2×Dic3—182no—
741C2×Dic3—361no—
742C2×Dic3—361no—
743C2×Dic3—361no—
744C2×Dic3—361no—
745C2×Dic3—361no—
746C2×Dic3C2×D3211yescharacteristic
747C2×Dic3C2×D3211yescharacteristic
748C2×Dic3C2×D3211yescharacteristic
749C2×Dic3C2×D3211yescharacteristic
750C2×Dic3C2×D3211yescharacteristic
751C2×Dic3C2×D3211yescharacteristic
752D12—94no—
753C4×D3—62no—
754C4×D3—62no—
755C4×D3—121no—
756C4×D3—121no—
757C4×D3—122no—
758C4×D3—182no—
759C4×D3—182no—
760C4×D3—184no—
761C4×D3—361no—
762C4×D3—361no—
763C4×D3—361no—
764C4×D3—361no—
765C4×D3—361no—
766C4×D3—361no—
767C4×D3—362no—
768C4×D3—362no—
769Dic6—41no—
770Dic6—62no—
771Dic6—62no—
772Dic6—121no—
773Dic6—121no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—41no—
784C2×C32—41no—
785C2×C32—41no—
786C2×C32C2×#23711yescharacteristic
787C2×C32#100411yescharacteristic
788C2×C32#100411yescharacteristic
789C2×C32C2×D3×Q811yescharacteristic
790C2×C32C2×D3×Q811yescharacteristic
791C2×C32C2×D3×Q811yescharacteristic
792C2×C32C2×#23911yescharacteristic
793C2×C32D3×#4111yescharacteristic
794C2×C32#100911yescharacteristic
795C3⋊D3—22no—
796C3⋊D3—22no—
797C3×D3—64no—
798C3×D3—62no—
799C3×D3—62no—
800C3×D3—62no—
801C3×D3—62no—
802C3×D3—122no—
803C2×Q8—31no—
804C2×Q8—91no—
805C2×Q8—91no—
806C2×D4—271no—
807C22×C4—91no—
808C22×C4—91no—
809C22×C4—271no—
810C22×C4—271no—
811C22×C4—271no—
812C22×C4—271no—
813C4⋊C4—31no—
814C4⋊C4—31no—
815C4⋊C4—91no—
816C4⋊C4—91no—
817C4⋊C4—91no—
818C4⋊C4—91no—
819C4⋊C4—91no—
820C4⋊C4—91no—
821C4⋊C4—271no—
822C4⋊C4—271no—
823C4⋊C4—271no—
824C4⋊C4—271no—
825C4⋊C4—271no—
826C4⋊C4—271no—
827C4⋊C4—271no—
828C4⋊C4—271no—
829C22⋊C4—91no—
830C22⋊C4—91no—
831C22⋊C4—91no—
832C22⋊C4—91no—
833C22⋊C4—271no—
834C22⋊C4—271no—
835C42—91no—
836C42—271no—
837C42—271no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—41no—
842C22×C3—92no—
843C22×C3—92no—
844C22×C3—181no—
845C22×C3—181no—
846C22×C3—181no—
847C22×C3—181no—
848C22×C3C22×D3211yescharacteristic
849C22×C3C22×D3211yescharacteristic
850C22×C3C22×D3211yescharacteristic
851C2×D3—32no—
852C2×D3—32no—
853C2×D3—32no—
854C2×D3—32no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—121no—
868C2×D3—121no—
869C3×C4—21no—
870C3×C4—21no—
871C3×C4—21no—
872C3×C4—32no—
873C3×C4—32no—
874C3×C4—41no—
875C3×C4—41no—
876C3×C4—41no—
877C3×C4—62no—
878C3×C4—62no—
879C3×C4—61no—
880C3×C4—61no—
881C3×C4—61no—
882C3×C4—61no—
883C3×C4—61no—
884C3×C4—61no—
885C3×C4—61no—
886C3×C4—61no—
887C3×C4—61no—
888C3×C4—61no—
889C3×C4—81no—
890C3×C4—92no—
891C3×C4—121no—
892C3×C4—121no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4—181no—
896C3×C4—181no—
897C3×C4—181no—
898Dic3—21no—
899Dic3—21no—
900Dic3—21no—
901Dic3—21no—
902Dic3—21no—
903Dic3—32no—
904Dic3—32no—
905Dic3—62no—
906Dic3—61no—
907Dic3—61no—
908Dic3—61no—
909Dic3—61no—
910Dic3—61no—
911Dic3—61no—
912Dic3—121no—
913Dic3—121no—
914Dic3—121no—
915Dic3—182no—
916Dic3—181no—
917Dic3—181no—
918Dic3—181no—
919Dic3—181no—
920Dic3—181no—
921Dic3—181no—
922Dic3—361no—
923Dic3—361no—
924Dic3—361no—
925Dic3—361no—
926Dic3—361no—
927Dic3—362no—
928Dic3—721no—
929Dic3#379612yes—
930C32—21no—
931C32—21no—
932C32—21no—
933C32—41no—
934C32#563511yescharacteristic, complemented
935C32#563611yescharacteristic, complemented
936C32#573011yescharacteristic, complemented
937C23—91no—
938C23—91no—
939Q8—121no—
940Q8—182no—
941Q8—361no—
942D4—274no—
943C2×C4—31no—
944C2×C4—31no—
945C2×C4—31no—
946C2×C4—31no—
947C2×C4—31no—
948C2×C4—31no—
949C2×C4—91no—
950C2×C4—91no—
951C2×C4—91no—
952C2×C4—91no—
953C2×C4—182no—
954C2×C4—271no—
955C2×C4—271no—
956C2×C4—361no—
957C2×C4—542no—
958C2×C4—1081no—
959C2×C4—1081no—
960C2×C4—1081no—
961C2×C4D3311yescharacteristic
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—41no—
972C2×C3—41no—
973C2×C3—41no—
974C2×C3—182no—
975C2×C3—182no—
976C2×C3C2×#379611yescharacteristic
977C2×C3#6430711yescharacteristic
978C2×C3D3×#23711yescharacteristic
979C2×C3#6431411yescharacteristic
980C2×C3D32×Q811yescharacteristic
981C2×C3D32×Q811yescharacteristic
982C2×C3D32×Q811yescharacteristic
983C2×C3D3×#23911yescharacteristic
984C2×C3#6433011yescharacteristic
985D3—64no—
986D3—62no—
987D3—62no—
988D3—62no—
989D3—62no—
990D3—122no—
991C22—92no—
992C22—92no—
993C22—181no—
994C22—181no—
995C22—181no—
996C22—181no—
997C22C2×D3311yescharacteristic
998C4—21no—
999C4—32no—
1000C4—61no—
1001C4—61no—
1002C4—61no—
1003C4—61no—
1004C4—61no—
1005C4—92no—
1006C4—181no—
1007C4—181no—
1008C4—181no—
1009C4—541no—
1010C4—541no—
1011C3—21no—
1012C3—21no—
1013C3—21no—
1014C3—41no—
1015C3#1059439311yescharacteristic, complemented
1016C3#1059453511yescharacteristic, complemented
1017C3#1059537211yescharacteristic, complemented
1018C2—182no—
1019C2—182no—
1020C2D3×#379611yescharacteristic
1021C2#1172437811yescharacteristic
1022C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6295C22
hypercenterC2×C4D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723476C2semidirect
3. C3⋊D3×Dic3⋊C4C2semidirect
4. #11723412C2semidirect
5. C3×#63895C2semidirect
6. C3×#63871C2semidirect
7. C3×#63839C2semidirect
8. #11723017C2semidirect
9. #11722979C2semidirect
10. #11722974C2semidirect
11. #11722974C2semidirect
12. #11722940C2semidirect
15. #11722908C2semidirect
67. #63895D3semidirect
91. #63871D3semidirect
100. #63839D3semidirect
119. #6295Q8semidirect
669. C33#554semidirect
934. C32#5635semidirect
935. C32#5636semidirect
936. C32#5730semidirect
1015. C3#10594393semidirect
1016. C3#10594535semidirect
1017. C3#10595372semidirect

Maximal subgroups

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

subgroupindex
#117236842
#117234762
C3⋊D3×Dic3⋊C42
#117234122
C3×#638952
C3×#638712
C3×#638392
#117230172
#117229792
#117229742
#117229402
#117229382
#117229342
#117229082
#105953723
#105945353
#105943933