Finite Group Databasebeta

← #13178132

Subgroups — #13178132

Order 1728.

1106 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#64079C211yesmaximal, characteristic, complemented
3C3×C4×#634C211yesmaximal, characteristic, complemented
4#11723689C211yesmaximal, characteristic, complemented
5#11723686C212yesmaximal
6#11723683C212yesmaximal, complemented
7#11723676C212yesmaximal, complemented
8#11723674C211yesmaximal, characteristic, complemented
9#11723674C211yesmaximal, characteristic, complemented
10#11723669C212yesmaximal, complemented
11#11723667C211yesmaximal, characteristic, complemented
12#10593947—31nomaximal
13#10593920—31nomaximal
14#10593917—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×#634C2211yescharacteristic
19C2×#6294C2212yes—
20C33×C42C2211yescharacteristic
21C3×#3752C2211yescharacteristic
22C3×#3752C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2212yes—
28C3×#3750C2212yes—
29C3×#3750C2212yes—
30C3×C4×C3⋊Dic3C2212yes—
31#88815C2212yes—
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88814C2212yes—
36#88814C2212yes—
37#88813C2212yes—
38C4×C4⋊(C3⋊D3)D311yescharacteristic
39#64079D311yescharacteristic, complemented
40C4×#634D311yescharacteristic, complemented
41C3×C4×D12—31no—
42C3×C4×D12—31no—
43C3×C4×D12—61no—
44C3×#870—31no—
45C3×#870—31no—
46C3×#870—61no—
47C3×C4×Dic6—31no—
48C3×C4×Dic6—31no—
49C3×C4×Dic6—61no—
50#63900—31no—
51#63897—32no—
52D3×C4⋊Dic3—31no—
53D3×C4⋊Dic3—31no—
54#63884—32no—
55#63884—32no—
56#63878—32no—
57#63877—32no—
58#63871—31no—
59#63871—31no—
60#63868—32no—
61#63862—32no—
62#63859—32no—
63#63857—31no—
64#63857—31no—
65#63856—31no—
66#63856—31no—
67#63849—31no—
68#63847—32no—
69#63846—32no—
70#63845—32no—
71#63841—31no—
72#63841—31no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)—22no—
86C3×C4×C3⋊D3—22no—
87C3×C4×C3⋊D3—22no—
88C3×#634—22no—
89#6294—24no—
90#5694—91no—
91#5581—91no—
92#5541—91no—
93C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×#634C2×D311yescharacteristic
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—61no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—61no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—61no—
109C2×#624—32no—
110C2×D3×Dic3—32no—
111C2×D3×Dic3—32no—
112C32×C42—21no—
113C32×C42—21no—
114C32×C42—21no—
115C32×C42—41no—
116C32×C42C2×D311yescharacteristic
117C32×C42C2×D311yescharacteristic
118C32×C42C2×D311yescharacteristic
119#3752C2×D311yescharacteristic
120#3752C2×D311yescharacteristic
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic
123C4⋊(C3⋊Dic3)C2×D311yescharacteristic
124C4⋊(C3⋊Dic3)C2×D311yescharacteristic
125#3750C2×D312yes—
126#3750C2×D312yes—
127#3750C2×D312yes—
128C4×C3⋊Dic3C2×D312yes—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×(C2×D3)⋊C4—61no—
134C3×(C2×D3)⋊C4—61no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3—61no—
146C3×C4⋊Dic3—61no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—62no—
154C3×Dic3⋊C4—62no—
155C3×Dic3⋊C4—62no—
156C3×C4×Dic3—32no—
157C3×C4×Dic3—32no—
158C3×C4×Dic3—62no—
159#3724—32no—
160#3724—32no—
161#3724—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168#3722—32no—
169#3722—32no—
170#3722—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—32no—
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3#4112yes—
187C33×C4—21no—
188C33×C4—21no—
189C33×C4#4112yes—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×#125—91no—
197C3×C4×Q8—91no—
198C3×C4×D4—91no—
199#946—91no—
200#946—91no—
201#935—92no—
202#926—91no—
203C2×C4⋊Dic3—91no—
204#924—91no—
205#924—91no—
206#898—92no—
207#897—91no—
208#897—91no—
209#894—92no—
210#894—92no—
211#892—92no—
212#892—91no—
213#892—91no—
214D3×C4⋊C4—91no—
215D3×C4⋊C4—91no—
216#890—92no—
217#889—92no—
218#889—92no—
219#879—92no—
220#877—92no—
221#876—92no—
222C4×D12—31no—
223C4×D12—31no—
224C4×D12—61no—
225#872—92no—
226#870—31no—
227#870—31no—
228#870—61no—
229C4×Dic6—31no—
230C4×Dic6—31no—
231C4×Dic6—61no—
232C22×C3⋊D3C22×D311yescharacteristic
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3×D3—31no—
235C22×C3×D3—31no—
236C22×C3×D3—31no—
237C22×C3×D3—31no—
238C22×C3×D3—61no—
239C22×C3×D3—61no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—41no—
250C2×C32×C4—41no—
251C2×C32×C4—41no—
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D312yes—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C4⋊(C3⋊D3)—22no—
268C4×C3⋊D3—22no—
269C4×C3⋊D3—22no—
270#634—22no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C3×D12—62no—
290C3×D12—62no—
291C3×D12—64no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—122no—
297C3×C4×D3—122no—
298C3×Dic6—64no—
299C3×Dic6—62no—
300C3×Dic6—62no—
301#624—64no—
302D3×Dic3—64no—
303D3×Dic3—64no—
304#552—271noSylow
305C2×C33C2×#4111yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C2×C332−1+411yescharacteristic
308C3×C3⋊D3—22no—
309C3×C3⋊D3—41no—
310C2×C3×Q8—91no—
311C2×C3×D4—91no—
312C22×C3×C4—91no—
313C22×C3×C4—91no—
314C22×Dic3—92no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—92no—
325C2×C4×D3—92no—
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—92no—
331C3×C4⋊C4—92no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—92no—
336C3×C22⋊C4—91no—
337C3×C22⋊C4—91no—
338C3×C42—21no—
339C3×C42—21no—
340C3×C42—21no—
341C3×C42—41no—
342C3×C42—92no—
343C3×C42D3211yescharacteristic
344C3×C42D3211yescharacteristic
345C3×C42D3211yescharacteristic
346#217—92no—
347#217—92no—
348#217—92no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—92no—
358(C2×D3)⋊C4—92no—
359(C2×D3)⋊C4—92no—
360(C2×D3)⋊C4—92no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—92no—
374C4⋊Dic3—92no—
375C4⋊Dic3—92no—
376Dic3⋊C4—32no—
377Dic3⋊C4—32no—
378Dic3⋊C4—32no—
379Dic3⋊C4—32no—
380Dic3⋊C4—32no—
381Dic3⋊C4—32no—
382Dic3⋊C4—62no—
383Dic3⋊C4—62no—
384Dic3⋊C4—62no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387Dic3⋊C4—92no—
388Dic3⋊C4—92no—
389Dic3⋊C4—92no—
390Dic3⋊C4—92no—
391C4×Dic3—32no—
392C4×Dic3—32no—
393C4×Dic3—62no—
394C4×Dic3—92no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—41no—
401C22×C32C23×D311yescharacteristic
402C22×C32C23×D311yescharacteristic
403C22×C32C23×D311yescharacteristic
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3⋊D3—21no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3#23512yes—
410C2×C3×D3—32no—
411C2×C3×D3—32no—
412C2×C3×D3—62no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—62no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C2×C3×D3—61no—
424C2×C3×D3—121no—
425C2×C3×D3—121no—
426C2×C3×D3—121no—
427C2×C3×D3—121no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—22no—
437C32×C4—22no—
438C32×C4—22no—
439C32×C4—42no—
440C32×C4—41no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4—42no—
445C32×C4—42no—
446C32×C4#23512yes—
447C32×C4#23712yes—
448C32×C4#23912yes—
449C3⋊Dic3—22no—
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—22no—
453C3⋊Dic3—22no—
454C3⋊Dic3—22no—
455C3×Dic3—64no—
456C3×Dic3—62no—
457C3×Dic3—62no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—62no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—121no—
469C3×Dic3—121no—
470C3×Dic3—122no—
471C3×Dic3—122no—
472C3×Dic3—122no—
473#126—272no—
474#125—91no—
475#125—272no—
476#123—272no—
477C22⋊Q8—271no—
478C22⋊Q8—271no—
479C4×Q8—91no—
480C4×D4—91no—
481#117—272no—
482#117—271no—
483C2×C4⋊C4—271no—
484C33#55211yescharacteristic, complemented, Sylow
485C23×C3—91no—
486C23×C3—91no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—61no—
492C22×D3—61no—
493C3×Q8—182no—
494C3×D4—182no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—91no—
508C2×C3×C4—92no—
509C2×C3×C4—92no—
510C2×C3×C4—91no—
511C2×C3×C4—92no—
512C2×C3×C4—92no—
513C2×C3×C4—182no—
514C2×C3×C4—182no—
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523C2×C3×C4C2×D3211yescharacteristic
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—32no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—184no—
543D12—62no—
544D12—62no—
545D12—64no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—184no—
553C4×D3—184no—
554Dic6—64no—
555Dic6—62no—
556Dic6—62no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—41no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32C2×#23511yescharacteristic
570C2×C32C2×#23511yescharacteristic
571C2×C32C2×#23711yescharacteristic
572C2×C32C2×#23911yescharacteristic
573C2×C32#100711yescharacteristic
574C2×C32D3×#4111yescharacteristic
575C2×C32D3×#4111yescharacteristic
576C2×C32#101011yescharacteristic
577C2×C32#101011yescharacteristic
578C3⋊D3—22no—
579C3⋊D3—41no—
580C3×D3—62no—
581C3×D3—62no—
582C3×D3—122no—
583C3×D3—122no—
584C3×D3—121no—
585C3×D3—121no—
586C2×Q8—91no—
587C2×D4—91no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—272no—
591C4⋊C4—91no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C4⋊C4—92no—
595C4⋊C4—91no—
596C4⋊C4—92no—
597C4⋊C4—92no—
598C4⋊C4—272no—
599C4⋊C4—272no—
600C4⋊C4—272no—
601C22⋊C4—91no—
602C22⋊C4—91no—
603C22⋊C4—272no—
604C22⋊C4—272no—
605C22⋊C4—272no—
606C42—92no—
607C42—272no—
608C42#111311yescharacteristic
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—41no—
613C22×C3—92no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3C22×D3211yescharacteristic
620C22×C3C22×D3211yescharacteristic
621C22×C3C22×D3211yescharacteristic
622C2×D3—32no—
623C2×D3—32no—
624C2×D3—62no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—182no—
659C3×C4—182no—
660C3×C4—181no—
661C3×C4—181no—
662C3×C4—182no—
663C3×C4—182no—
664C3×C4#379512yes—
665C3×C4#379612yes—
666C3×C4#379912yes—
667Dic3—64no—
668Dic3—62no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—62no—
674Dic3—62no—
675Dic3—62no—
676Dic3—62no—
677Dic3—62no—
678Dic3—62no—
679Dic3—62no—
680Dic3—121no—
681Dic3—121no—
682Dic3—122no—
683Dic3—122no—
684Dic3—122no—
685C32—21no—
686C32—21no—
687C32—21no—
688C32—41no—
689C32#554111yescharacteristic, complemented
690C32#558111yescharacteristic, complemented
691C32#569411yescharacteristic, complemented
692C23—91no—
693C23—91no—
694Q8—182no—
695D4—182no—
696C2×C4—92no—
697C2×C4—92no—
698C2×C4—91no—
699C2×C4—92no—
700C2×C4—91no—
701C2×C4—92no—
702C2×C4—182no—
703C2×C4—182no—
704C2×C4—544no—
705C2×C4C2×#111311yescharacteristic
706C2×C4C2×#111311yescharacteristic
707C2×C4C2×#111311yescharacteristic
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—182no—
721C2×C3—361no—
722C2×C3C2×#379511yescharacteristic
723C2×C3C2×#379611yescharacteristic
724C2×C3#6429711yescharacteristic
725C2×C3#6429711yescharacteristic
726C2×C3#6429811yescharacteristic
727C2×C3C2×#379911yescharacteristic
728C2×C3D3×#23511yescharacteristic
729C2×C3D3×#23511yescharacteristic
730C2×C3#6430611yescharacteristic
731D3—62no—
732D3—62no—
733D3—122no—
734D3—122no—
735D3—121no—
736D3—121no—
737C22—92no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22C22×#111311yescharacteristic
744C4—21no—
745C4—21no—
746C4—181no—
747C4—181no—
748C4—182no—
749C4—182no—
750C4—182no—
751C4—182no—
752C4#8904112yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059391711yescharacteristic, complemented
758C3#1059392011yescharacteristic, complemented
759C3#1059394711yescharacteristic, complemented
760C2—182no—
761C2—361no—
762C2C2×#8904111yescharacteristic
763C2#1172461411yescharacteristic
764C2#1172461811yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC42#1113
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×#64079C2semidirect
3. C3×C4×#634C2semidirect
4. #11723689C2semidirect
6. #11723683C2semidirect
7. #11723676C2semidirect
8. #11723674C2semidirect
9. #11723674C2semidirect
10. #11723669C2semidirect
11. #11723667C2semidirect
39. #64079D3semidirect
40. C4×#634D3semidirect
484. C33#552semidirect
689. C32#5541semidirect
690. C32#5581semidirect
691. C32#5694semidirect
757. C3#10593917semidirect
758. C3#10593920semidirect
759. C3#10593947semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C4⋊(C3⋊D3)2
C3×#640792
C3×C4×#6342
#117236892
#117236862
#117236832
#117236762
#117236742
#117236692
#117236672
#105939473
#105939203
#105939173