Finite Group Databasebeta

← #13168744

Subgroups — #13168744

Order 1728.

1192 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723671C211yesmaximal, characteristic, complemented
2C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
3D3×#3750C211yesmaximal, characteristic, complemented
4#11723389C211yesmaximal, characteristic, complemented
5C3×C4×#626C211yesmaximal, characteristic
6C3×#63867C211yesmaximal, characteristic, complemented
7C3×#63851C211yesmaximal, characteristic, complemented
8#11723035C211yesmaximal, characteristic, complemented
9#11723013C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722981C211yesmaximal, characteristic, complemented
12#11722980C211yesmaximal, characteristic, complemented
13#11722974C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic
15#11722929C211yesmaximal, characteristic
16#10594959—31nomaximal
17#10594394—31nomaximal
18#10593941—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6296C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29#88857C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34#88815C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88807C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×#3750—31no—
55C4⋊C4×C3⋊D3—31no—
56C4×#634—31no—
57C3×C4×#67—31no—
58C3×#924—31no—
59C3×#896—31no—
60C3×#889—31no—
61C3×C4×D12—31no—
62C3×#870—31no—
63#63982—31no—
64#63982—31no—
65#67⋊Dic3—31no—
66#67⋊Dic3—31no—
67#63919—31no—
68C4×#626D311yescharacteristic
69#63899—31no—
70#63899—31no—
71#63898—31no—
72#63898—31no—
73#63896—31no—
74#63896—31no—
75#63893—31no—
76#63893—31no—
77#63893—31no—
78#63887—31no—
79#63881—31no—
80#63881—31no—
81D3×Dic3⋊C4—31no—
82D3×Dic3⋊C4—31no—
83D3×Dic3⋊C4—31no—
84D3×Dic3⋊C4—31no—
85D3×Dic3⋊C4—61no—
86D3×Dic3⋊C4—61no—
87#63872—31no—
88#63871—31no—
89#63867D311yescharacteristic, complemented
90#63865—31no—
91#63865—31no—
92#63851—31no—
93#63851—31no—
94#63851D311yescharacteristic, complemented
95#63846—31no—
96#63845—31no—
97#63839—31no—
98#63839—31no—
99#63837—31no—
100#63837—31no—
101#63837—61no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×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
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4×C3⋊D3—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—41no—
119#6296—41no—
120#6293—22no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3—41no—
123D3×C3⋊Dic3—22no—
124D3×C3⋊Dic3—41no—
125C3×#627—41no—
126C3×#626Q814yescomplemented
127#5690—91no—
128#5636—91no—
129#5539—91no—
130C22×C32×C4—31no—
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3C2×D311yescharacteristic
136C2×#634—31no—
137C2×C3×#67—31no—
138C2×C3×D12—31no—
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—61no—
143C2×C3×C4×D3C2×D311yescharacteristic
144C2×C3×C4×D3C2×D311yescharacteristic
145C2×C3×Dic6—31no—
146C2×C3×Dic6—31no—
147C2×#627—31no—
148C2×#627—31no—
149C2×#627—31no—
150C2×#627—31no—
151C2×#627—31no—
152C2×#627—61no—
153C2×#627C2×D311yescharacteristic
154C2×#626C2×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—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—61no—
164C2×D3×Dic3—61no—
165C2×D3×Dic3—61no—
166C2×D3×Dic3—61no—
167C32×C4⋊C4—31no—
168C32×C42—31no—
169C4⋊(C3⋊Dic3)—31no—
170C4⋊(C3⋊Dic3)—31no—
171#3750—31no—
172#3750—31no—
173#3750—31no—
174#3750—31no—
175#3750—31no—
176#3750—31no—
177#3750—61no—
178#3750—61no—
179#3750—61no—
180#3750—121no—
181#3750C2×D311yescharacteristic
182#3750C2×D311yescharacteristic
183C4×C3⋊Dic3—31no—
184C4×C3⋊Dic3—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—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×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×Dic3⋊C4—21no—
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⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4C2×D311yescharacteristic
213C3×Dic3⋊C4C2×D311yescharacteristic
214C3×C4×Dic3—21no—
215C3×C4×Dic3C2×D311yescharacteristic
216C3×C4×Dic3C2×D311yescharacteristic
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—31no—
222#3724—61no—
223#3724—61no—
224#3724C2×D311yescharacteristic
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241#3722—31no—
242#3722—31no—
243#3722C2×D311yescharacteristic
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32—61no—
257C22×C33C2411yescharacteristic
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C3×C3⋊D3C2×Q812yes—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3C2×Q812yes—
264C33×C4—21no—
265C3⋊(C3⋊Dic3)—21no—
266C3⋊(C3⋊Dic3)#4112yes—
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×Dic3C2×Q812yes—
277C3×#125—91no—
278C3×C22⋊Q8—91no—
279C3×C4×D4—91no—
280#946—91no—
281#944—91no—
282D4×Dic3—91no—
283D4×Dic3—91no—
284C4×#67—31no—
285#924—31no—
286#924—91no—
287C2×Dic3⋊C4—91no—
288C2×Dic3⋊C4—91no—
289C2×Dic3⋊C4—91no—
290C2×Dic3⋊C4—181no—
291#897—91no—
292#897—91no—
293#896—31no—
294#896—91no—
295#896—91no—
296#896—91no—
297#896—91no—
298#896—91no—
299#893—91no—
300#893—91no—
301D3×C4⋊C4—91no—
302D3×C4⋊C4—91no—
303D3×C4⋊C4—91no—
304D3×C4⋊C4—181no—
305#890—91no—
306#890—91no—
307#889—31no—
308#889—91no—
309#888—91no—
310#888—91no—
311#887—91no—
312#67⋊C4—91no—
313#67⋊C4—91no—
314#878—91no—
315#878—91no—
316#878—91no—
317#878—91no—
318#878—91no—
319#878—91no—
320C4×D12—31no—
321#870—31no—
322C4×Dic6—91no—
323C4×Dic6—91no—
324C4×Dic6—181no—
325C23×C32—31no—
326C22×C3⋊D3C22×D311yescharacteristic
327C22×C3×D3—21no—
328C22×C3×D3—31no—
329C22×C3×D3—31no—
330C22×C3×D3—61no—
331C22×C3×D3C22×D311yescharacteristic
332C22×C3×D3C22×D311yescharacteristic
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—41no—
342C2×C32×C4—121no—
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—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—61no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—62no—
359C2×C3⋊Dic3—121no—
360C2×C3⋊Dic3—121no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C4×C3⋊D3—41no—
368C4×C3⋊D3—62no—
369C4×C3⋊D3—121no—
370#634—62no—
371C3×#67—34no—
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—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
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×D12—34no—
403C3×C4×D3—41no—
404C3×C4×D3—41no—
405C3×C4×D3—42no—
406C3×C4×D3—121no—
407C3×C4×D3—121no—
408C3×C4×D3—122no—
409C3×Dic6—121no—
410C3×Dic6—121no—
411#627—41no—
412#627—62no—
413#627—62no—
414#627—64no—
415#627—121no—
416#627—121no—
417#627—121no—
418#626Dic614yescomplemented
419D3×Dic3—62no—
420D3×Dic3—62no—
421D3×Dic3—64no—
422D3×Dic3—62no—
423D3×Dic3—62no—
424D3×Dic3—64no—
425D3×Dic3—121no—
426D3×Dic3—121no—
427D3×Dic3—122no—
428D3×Dic3—121no—
429D3×Dic3—121no—
430D3×Dic3—122no—
431#554—271noSylow
432C2×C33C22×Q811yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C2×C33H(5,𝔽2)11yescharacteristic
435C3×C3⋊D3—22no—
436C32×D3—22no—
437C2×C3×Q8—91no—
438C2×C3×D4—91no—
439C22×C3×C4—31no—
440C22×C3×C4—31no—
441C22×C3×C4—61no—
442C22×C3×C4—91no—
443C2×#67—31no—
444C22×Dic3—91no—
445C22×Dic3—91no—
446C22×Dic3—91no—
447C22×Dic3—91no—
448C22×Dic3—91no—
449C22×Dic3—91no—
450C22×Dic3—181no—
451C22×Dic3—181no—
452C2×D12—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—61no—
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×D3D3211yescharacteristic
465C2×Dic6—31no—
466C2×Dic6—31no—
467C2×Dic6—91no—
468C2×Dic6—91no—
469C2×Dic6—91no—
470C2×Dic6—91no—
471C2×Dic6—91no—
472C2×Dic6—91no—
473C2×Dic6—181no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—31no—
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×C22⋊C4—91no—
489C3×C42—31no—
490C3×C42—31no—
491C3×C42—61no—
492#217—31no—
493#217—31no—
494#217—31no—
495#217—91no—
496#217—91no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506C4⋊Dic3—31no—
507C4⋊Dic3—31no—
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—31no—
511C4⋊Dic3—91no—
512C4⋊Dic3—91no—
513C4⋊Dic3—91no—
514C4⋊Dic3—91no—
515C4⋊Dic3—91no—
516C4⋊Dic3—91no—
517C4⋊Dic3—181no—
518C4⋊Dic3—181no—
519Dic3⋊C4—31no—
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—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—61no—
531Dic3⋊C4—61no—
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—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—181no—
548Dic3⋊C4—181no—
549Dic3⋊C4—181no—
550Dic3⋊C4—181no—
551Dic3⋊C4—181no—
552Dic3⋊C4—181no—
553Dic3⋊C4—361no—
554Dic3⋊C4D3211yescharacteristic
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—181no—
562C4×Dic3—181no—
563C4×Dic3D3211yescharacteristic
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—32no—
568C22×C32—41no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3C2×Dic612yes—
577C2×C3×D3—22no—
578C2×C3×D3—22no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—22no—
584C2×C3×D3—32no—
585C2×C3×D3—32no—
586C2×C3×D3—62no—
587C2×C3×D3—62no—
588C2×C3×D3—62no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3C2×Dic612yes—
594C2×C3×D3D3×Q812yes—
595C32×C4—21no—
596C32×C4—21no—
597C32×C4—21no—
598C32×C4—32no—
599C32×C4—41no—
600C32×C4—41no—
601C32×C4—41no—
602C32×C4—61no—
603C32×C4—61no—
604C32×C4—61no—
605C32×C4—61no—
606C32×C4—81no—
607C3⋊Dic3—21no—
608C3⋊Dic3—21no—
609C3⋊Dic3—21no—
610C3⋊Dic3—21no—
611C3⋊Dic3—21no—
612C3⋊Dic3—32no—
613C3⋊Dic3—32no—
614C3⋊Dic3—32no—
615C3⋊Dic3—62no—
616C3⋊Dic3—62no—
617C3⋊Dic3—62no—
618C3⋊Dic3—61no—
619C3⋊Dic3—61no—
620C3⋊Dic3—61no—
621C3⋊Dic3—122no—
622C3⋊Dic3—121no—
623C3⋊Dic3—121no—
624C3⋊Dic3—121no—
625C3⋊Dic3—241no—
626C3×Dic3—22no—
627C3×Dic3—22no—
628C3×Dic3—21no—
629C3×Dic3—21no—
630C3×Dic3—21no—
631C3×Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—22no—
637C3×Dic3—41no—
638C3×Dic3—41no—
639C3×Dic3—62no—
640C3×Dic3—62no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—121no—
652C3×Dic3—121no—
653C3×Dic3—121no—
654C3×Dic3C2×Dic612yes—
655C3×Dic3D3×Q812yes—
656C4⋊Q8—271no—
657#125—91no—
658#125—271no—
659C22⋊Q8—91no—
660C22⋊Q8—271no—
661C22⋊Q8—271no—
662C22⋊Q8—271no—
663C22⋊Q8—271no—
664C22⋊Q8—271no—
665C4×Q8—271no—
666C4×D4—91no—
667C4×D4—271no—
668C4×D4—271no—
669C2×C4⋊C4—271no—
670C2×C4⋊C4—271no—
671C33#55411yescharacteristic, complemented, Sylow
672C23×C3—31no—
673C23×C3—31no—
674C23×C3—61no—
675C23×C3—91no—
676C22×D3—31no—
677C22×D3—31no—
678C22×D3—61no—
679C22×D3C2×D3211yescharacteristic
680C3×Q8—361no—
681C3×D4—94no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—31no—
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—41no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—91no—
702C2×C3×C4—91no—
703C2×C3×C4—91no—
704C2×C3×C4—91no—
705C2×C3×C4—91no—
706C2×C3×C4—121no—
707C2×C3×C4—121no—
708C2×C3×C4—122no—
709C2×C3×C4—361no—
710C2×C3×C4C2×D3211yescharacteristic
711C2×C3×C4C2×D3211yescharacteristic
712C2×C3×C4C2×D3211yescharacteristic
713#67—34no—
714C2×Dic3—31no—
715C2×Dic3—31no—
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—61no—
729C2×Dic3—91no—
730C2×Dic3—91no—
731C2×Dic3—91no—
732C2×Dic3—91no—
733C2×Dic3—91no—
734C2×Dic3—91no—
735C2×Dic3—181no—
736C2×Dic3—181no—
737C2×Dic3—181no—
738C2×Dic3—181no—
739C2×Dic3—181no—
740C2×Dic3—181no—
741C2×Dic3—182no—
742C2×Dic3—182no—
743C2×Dic3—182no—
744C2×Dic3—184no—
745C2×Dic3—361no—
746C2×Dic3—361no—
747C2×Dic3—361no—
748C2×Dic3—361no—
749C2×Dic3—361no—
750C2×Dic3—362no—
751C2×Dic3C2×D3211yescharacteristic
752C2×Dic3C2×D3211yescharacteristic
753C2×Dic3C2×D3211yescharacteristic
754C2×Dic3C2×D3211yescharacteristic
755C2×Dic3C2×D3211yescharacteristic
756D12—34no—
757C4×D3—41no—
758C4×D3—121no—
759C4×D3—121no—
760C4×D3—122no—
761C4×D3—182no—
762C4×D3—182no—
763C4×D3—182no—
764C4×D3—184no—
765C4×D3—361no—
766C4×D3—361no—
767C4×D3—361no—
768C4×D3—362no—
769Dic6—121no—
770Dic6—121no—
771Dic6—182no—
772Dic6—182no—
773Dic6—182no—
774Dic6—184no—
775Dic6—361no—
776Dic6—361no—
777Dic6—361no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—41no—
788C2×C32—41no—
789C2×C32—41no—
790C2×C32—62no—
791C2×C32C22×Dic611yescharacteristic
792C2×C32#100411yescharacteristic
793C2×C32#100411yescharacteristic
794C2×C32C2×D3×Q811yescharacteristic
795C2×C32C2×D3×Q811yescharacteristic
796C2×C32D3×#4111yescharacteristic
797C2×C32D3×#4111yescharacteristic
798C2×C32D3×#4111yescharacteristic
799C2×C32#100911yescharacteristic
800C3⋊D3—22no—
801C3×D3—24no—
802C3×D3—22no—
803C3×D3—22no—
804C3×D3—64no—
805C3×D3—62no—
806C3×D3—62no—
807C2×Q8—91no—
808C2×Q8—271no—
809C2×Q8—271no—
810C2×D4—91no—
811C22×C4—31no—
812C22×C4—91no—
813C22×C4—271no—
814C22×C4—271no—
815C22×C4—271no—
816C22×C4—271no—
817C4⋊C4—31no—
818C4⋊C4—91no—
819C4⋊C4—91no—
820C4⋊C4—91no—
821C4⋊C4—91no—
822C4⋊C4—91no—
823C4⋊C4—91no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—271no—
827C4⋊C4—271no—
828C4⋊C4—271no—
829C4⋊C4—271no—
830C4⋊C4—271no—
831C4⋊C4—271no—
832C4⋊C4—271no—
833C22⋊C4—91no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—271no—
838C22⋊C4—271no—
839C42—31no—
840C42—271no—
841C42—271no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—32no—
846C22×C3—32no—
847C22×C3—41no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—92no—
856C22×C3—181no—
857C22×C3—181no—
858C22×C3C22×D3211yescharacteristic
859C22×C3C22×D3211yescharacteristic
860C22×C3C22×D3211yescharacteristic
861C2×D3—21no—
862C2×D3—21no—
863C2×D3—32no—
864C2×D3—32no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3D3×Dic612yes—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—32no—
877C3×C4—32no—
878C3×C4—41no—
879C3×C4—41no—
880C3×C4—41no—
881C3×C4—62no—
882C3×C4—62no—
883C3×C4—62no—
884C3×C4—61no—
885C3×C4—61no—
886C3×C4—61no—
887C3×C4—61no—
888C3×C4—61no—
889C3×C4—61no—
890C3×C4—61no—
891C3×C4—61no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4—181no—
896C3×C4—181no—
897C3×C4—181no—
898C3×C4—181no—
899C3×C4—181no—
900Dic3—21no—
901Dic3—21no—
902Dic3—21no—
903Dic3—21no—
904Dic3—62no—
905Dic3—62no—
906Dic3—61no—
907Dic3—61no—
908Dic3—61no—
909Dic3—61no—
910Dic3—61no—
911Dic3—61no—
912Dic3—61no—
913Dic3—61no—
914Dic3—61no—
915Dic3—61no—
916Dic3—92no—
917Dic3—92no—
918Dic3—92no—
919Dic3—121no—
920Dic3—121no—
921Dic3—121no—
922Dic3—182no—
923Dic3—182no—
924Dic3—182no—
925Dic3—181no—
926Dic3—181no—
927Dic3—181no—
928Dic3—362no—
929Dic3—361no—
930Dic3—361no—
931Dic3—361no—
932Dic3—721no—
933Dic3D3×Dic612yes—
934C32—21no—
935C32—21no—
936C32—21no—
937C32—41no—
938C32#553911yescharacteristic, complemented
939C32#563611yescharacteristic, complemented
940C32#569011yescharacteristic, complemented
941C23—31no—
942C23—91no—
943Q8—361no—
944Q8—542no—
945Q8—1081no—
946D4—94no—
947C2×C4—31no—
948C2×C4—31no—
949C2×C4—31no—
950C2×C4—31no—
951C2×C4—31no—
952C2×C4—91no—
953C2×C4—91no—
954C2×C4—91no—
955C2×C4—91no—
956C2×C4—91no—
957C2×C4—121no—
958C2×C4—271no—
959C2×C4—271no—
960C2×C4—361no—
961C2×C4—542no—
962C2×C4—542no—
963C2×C4—1081no—
964C2×C4—1081no—
965C2×C4D3311yescharacteristic
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—41no—
976C2×C3—41no—
977C2×C3—41no—
978C2×C3—64no—
979C2×C3—62no—
980C2×C3—62no—
981C2×C3—182no—
982C2×C3C2×D3×Dic611yescharacteristic
983C2×C3C2×D3×Dic611yescharacteristic
984C2×C3#6430611yescharacteristic
985C2×C3#6430611yescharacteristic
986C2×C3#6430611yescharacteristic
987C2×C3#6430711yescharacteristic
988C2×C3#6431411yescharacteristic
989C2×C3D32×Q811yescharacteristic
990C2×C3#6433011yescharacteristic
991D3—22no—
992D3—64no—
993D3—62no—
994D3—62no—
995C22—32no—
996C22—61no—
997C22—61no—
998C22—92no—
999C22—181no—
1000C22—181no—
1001C22C2×D3311yescharacteristic
1002C4—21no—
1003C4—32no—
1004C4—61no—
1005C4—61no—
1006C4—61no—
1007C4—61no—
1008C4—181no—
1009C4—181no—
1010C4—181no—
1011C4—181no—
1012C4—181no—
1013C4—272no—
1014C4—541no—
1015C3—21no—
1016C3—21no—
1017C3—21no—
1018C3—41no—
1019C3#1059394111yescharacteristic, complemented
1020C3#1059439411yescharacteristic, complemented
1021C3#1059495911yescharacteristic, complemented
1022C2—62no—
1023C2—182no—
1024C2D32×Dic611yescharacteristic
1025C2#1172439811yescharacteristic
1026C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#626C22
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
1. #11723671C2semidirect
2. C3⋊D3×Dic3⋊C4C2semidirect
3. D3×#3750C2semidirect
4. #11723389C2semidirect
6. C3×#63867C2semidirect
7. C3×#63851C2semidirect
8. #11723035C2semidirect
9. #11723013C2semidirect
10. #11722983C2semidirect
11. #11722981C2semidirect
12. #11722980C2semidirect
13. #11722974C2semidirect
89. #63867D3semidirect
94. #63851D3semidirect
126. C3×#626Q8semidirect
418. #626Dic6semidirect
671. C33#554semidirect
938. C32#5539semidirect
939. C32#5636semidirect
940. C32#5690semidirect
1019. C3#10593941semidirect
1020. C3#10594394semidirect
1021. C3#10594959semidirect

Maximal subgroups

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

subgroupindex
#117236712
C3⋊D3×Dic3⋊C42
D3×#37502
#117233892
C3×C4×#6262
C3×#638672
C3×#638512
#117230352
#117230132
#117229832
#117229812
#117229802
#117229742
#117229292
#105949593
#105943943
#105939413