Finite Group Databasebeta

← #13178136

Subgroups — #13178136

Order 1728.

1162 conjugacy classes of subgroups.

The subgroup lattice has 742 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
4C4⋊#6296C211yesmaximal, characteristic, complemented
5#11723692C212yesmaximal, complemented
6#11723691C211yesmaximal, characteristic
7#11723691C211yesmaximal, characteristic
8#11723688C212yesmaximal, complemented
9#11723682C212yesmaximal, complemented
10#11723680C211yesmaximal, characteristic, complemented
11#11723671C212yesmaximal, complemented
12#10593941—31nomaximal
13#10593938—31nomaximal
14#10593929—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2212yes—
17C2×C3×#634C2211yescharacteristic
18C2×#6296C2212yes—
19C2×#6294C2212yes—
20C2×#6294C2212yes—
21C33×C42C2211yescharacteristic
22C3×#3752C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C3×#3750C2212yes—
30C3×#3750C2212yes—
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C3×C4×C3⋊Dic3C2211yescharacteristic
33#88815C2212yes—
34#88815C2212yes—
35#88815C2212yes—
36#88814C2212yes—
37#88814C2212yes—
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#63919—31no—
51#63918—31no—
52#63918—31no—
53#63899—32no—
54#63898—31no—
55#63898—31no—
56#63896—32no—
57#63895—32no—
58#63894—31no—
59#63894—31no—
60#63893—32no—
61Dic3×D12—31no—
62Dic3×D12—31no—
63#63888—32no—
64#63887—32no—
65#63883—32no—
66D3×Dic3⋊C4—32no—
67D3×Dic3⋊C4—32no—
68#63872—31no—
69#63869—31no—
70#63869—31no—
71#63865—32no—
72#63851—32no—
73#63851—32no—
74C22×C3×C3⋊D3C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)Q814yescomplemented
86C3×C4×C3⋊D3—42no—
87C3×#634—22no—
88#6296—42no—
89#6294—24no—
90#6294—42no—
91#5690—91no—
92#5579—91no—
93#5539—91no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×C4×C3⋊D3C2×D312yes—
96C2×#634C2×D311yescharacteristic
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—61no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3—62no—
103C2×C3×Dic6—31no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—61no—
106C2×#627—32no—
107C2×#627—32no—
108C2×#627—32no—
109C2×#624—32no—
110C2×#624—32no—
111C2×D3×Dic3—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114C2×D3×Dic3—32no—
115C32×C42—21no—
116C32×C42—21no—
117C32×C42—21no—
118C32×C42—41no—
119C32×C42C2×D311yescharacteristic
120C32×C42C2×D311yescharacteristic
121C32×C42C2×D311yescharacteristic
122#3752C2×D312yes—
123C4⋊(C3⋊Dic3)C2×D311yescharacteristic
124C4⋊(C3⋊Dic3)C2×D311yescharacteristic
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126C4⋊(C3⋊Dic3)C2×D311yescharacteristic
127#3750C2×D311yescharacteristic
128#3750C2×D311yescharacteristic
129#3750C2×D312yes—
130#3750C2×D312yes—
131C4×C3⋊Dic3C2×D311yescharacteristic
132C4×C3⋊Dic3C2×D311yescharacteristic
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—62no—
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—31no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3—61no—
146C3×C4⋊Dic3—61no—
147C3×C4⋊Dic3—61no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—31no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—61no—
157C3×Dic3⋊C4—61no—
158C3×Dic3⋊C4—62no—
159C3×Dic3⋊C4—62no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—61no—
165C3×C4×Dic3—61no—
166#3724—32no—
167#3724—32no—
168#3724—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3—32no—
175#3722—32no—
176#3722—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—32no—
181C22×C33C2411yescharacteristic
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3C2×Q814yes—
185C33×C4—21no—
186C33×C4—21no—
187C33×C4C2×Q812yes—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—22no—
194C3×C3⋊Dic3#4112yes—
195C3×#125—91no—
196C3×C4×Q8—91no—
197C3×C4×D4—91no—
198#946—92no—
199D4×Dic3—91no—
200D4×Dic3—91no—
201#924—92no—
202C2×Dic3⋊C4—92no—
203#897—92no—
204#896—92no—
205#896—92no—
206#896—92no—
207#896—92no—
208#893—91no—
209#893—91no—
210D3×C4⋊C4—92no—
211D3×C4⋊C4—92no—
212#890—91no—
213#890—91no—
214#888—91no—
215#888—91no—
216#878—92no—
217#878—92no—
218C4×D12—31no—
219C4×D12—31no—
220C4×D12—61no—
221C4×D12—91no—
222C4×D12—91no—
223#870—31no—
224#870—31no—
225#870—61no—
226#870—91no—
227#869—91no—
228C4×Dic6—31no—
229C4×Dic6—31no—
230C4×Dic6—61no—
231C22×C3⋊D3C22×D312yes—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—62no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—41no—
245C2×C32×C4—41no—
246C2×C32×C4—41no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D312yes—
259C2×C3⋊Dic3C22×D312yes—
260C2×C3⋊Dic3C22×D312yes—
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C4⋊(C3⋊D3)Dic614yescomplemented
264C4×C3⋊D3—42no—
265#634—22no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C3×D12—34no—
288C3×D12—34no—
289C3×D12—64no—
290C3×C4×D3—122no—
291C3×C4×D3—122no—
292C3×C4×D3—124no—
293C3×Dic6—62no—
294C3×Dic6—62no—
295C3×Dic6—64no—
296#627—122no—
297#627—122no—
298#627—122no—
299#624—64no—
300#624—122no—
301D3×Dic3—64no—
302D3×Dic3—64no—
303D3×Dic3—122no—
304D3×Dic3—122no—
305#554—271noSylow
306C2×C33C22×Q811yescharacteristic
307C2×C33C2×#4111yescharacteristic
308C2×C33H(5,𝔽2)11yescharacteristic
309C3×C3⋊D3—24no—
310C2×C3×Q8—91no—
311C2×C3×D4—91no—
312C22×C3×C4—92no—
313C22×Dic3—92no—
314C22×Dic3—92no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×C4×D3—32no—
319C2×C4×D3—32no—
320C2×C4×D3—62no—
321C2×C4×D3—92no—
322C2×C4×D3—92no—
323C2×C4×D3—92no—
324C2×C4×D3—92no—
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—61no—
328C2×Dic6—92no—
329C2×Dic6—92no—
330C2×Dic6—92no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—92no—
336C3×C4⋊C4—91no—
337C3×C4⋊C4—91no—
338C3×C4⋊C4—92no—
339C3×C22⋊C4—92no—
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—41no—
344C3×C42—91no—
345C3×C42—91no—
346C3×C42D3211yescharacteristic
347C3×C42D3211yescharacteristic
348C3×C42D3211yescharacteristic
349#217—92no—
350#217—92no—
351(C2×D3)⋊C4—32no—
352(C2×D3)⋊C4—32no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—92no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—92no—
371C4⋊Dic3—92no—
372C4⋊Dic3—92no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—32no—
378Dic3⋊C4—32no—
379Dic3⋊C4—32no—
380Dic3⋊C4—32no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
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—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—41no—
401C22×C32C23×D311yescharacteristic
402C22×C32C23×D311yescharacteristic
403C22×C32C23×D311yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3C2×Dic614yes—
407C2×C3×D3—34no—
408C2×C3×D3—34no—
409C2×C3×D3—64no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—122no—
415C2×C3×D3—122no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—22no—
419C32×C4—22no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—22no—
425C32×C4—22no—
426C32×C4—22no—
427C32×C4—42no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4—42no—
433C32×C4—42no—
434C32×C4C2×Dic612yes—
435C32×C4D3×Q812yes—
436C32×C4D3×Q812yes—
437C3⋊Dic3—21no—
438C3⋊Dic3—22no—
439C3⋊Dic3—22no—
440C3⋊Dic3—21no—
441C3⋊Dic3—22no—
442C3⋊Dic3—21no—
443C3⋊Dic3#23512yes—
444C3×Dic3—32no—
445C3×Dic3—32no—
446C3×Dic3—62no—
447C3×Dic3—62no—
448C3×Dic3—62no—
449C3×Dic3—61no—
450C3×Dic3—62no—
451C3×Dic3—61no—
452C3×Dic3—62no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—62no—
457C3×Dic3—61no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—122no—
461C3×Dic3—122no—
462C3×Dic3—121no—
463C3×Dic3—122no—
464C3×Dic3—121no—
465C4⋊Q8—271no—
466#125—91no—
467#125—271no—
468C22⋊Q8—272no—
469C22⋊Q8—272no—
470C22⋊Q8—272no—
471C4×Q8—91no—
472C4×D4—91no—
473C4×D4—271no—
474C4×D4—271no—
475C2×C4⋊C4—272no—
476C33#55411yescharacteristic, complemented, Sylow
477C23×C3—92no—
478C22×D3—32no—
479C22×D3—32no—
480C22×D3—62no—
481C3×Q8—182no—
482C3×D4—94no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—91no—
496C2×C3×C4—92no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—92no—
500C2×C3×C4—92no—
501C2×C3×C4—91no—
502C2×C3×C4—362no—
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507C2×C3×C4C2×D3211yescharacteristic
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×C3×C4C2×D3211yescharacteristic
511C2×C3×C4C2×D3211yescharacteristic
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—32no—
523C2×Dic3—32no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—184no—
534C2×Dic3—362no—
535D12—34no—
536D12—34no—
537D12—64no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—124no—
541C4×D3—184no—
542C4×D3—184no—
543C4×D3—362no—
544C4×D3—362no—
545Dic6—62no—
546Dic6—62no—
547Dic6—64no—
548Dic6—362no—
549Dic6—362no—
550Dic6—362no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—41no—
561C2×C32—41no—
562C2×C32—41no—
563C2×C32C22×Dic611yescharacteristic
564C2×C32C2×#23511yescharacteristic
565C2×C32#100411yescharacteristic
566C2×C32C2×D3×Q811yescharacteristic
567C2×C32C2×D3×Q811yescharacteristic
568C2×C32D3×#4111yescharacteristic
569C2×C32D3×#4111yescharacteristic
570C2×C32#100911yescharacteristic
571C2×C32#100911yescharacteristic
572C3⋊D3—24no—
573C3×D3—64no—
574C3×D3—64no—
575C3×D3—124no—
576C2×Q8—91no—
577C2×Q8—272no—
578C2×D4—91no—
579C22×C4—92no—
580C22×C4—272no—
581C22×C4—272no—
582C4⋊C4—91no—
583C4⋊C4—92no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—91no—
588C4⋊C4—91no—
589C4⋊C4—92no—
590C4⋊C4—272no—
591C4⋊C4—272no—
592C4⋊C4—272no—
593C22⋊C4—92no—
594C22⋊C4—272no—
595C22⋊C4—272no—
596C42—91no—
597C42—91no—
598C42#111311yescharacteristic
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—41no—
603C22×C3—94no—
604C22×C3—182no—
605C22×C3—182no—
606C22×C3C22×D3211yescharacteristic
607C22×C3C22×D3211yescharacteristic
608C22×C3C22×D3211yescharacteristic
609C2×D3—34no—
610C2×D3—34no—
611C2×D3—64no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—122no—
617C2×D3—122no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—92no—
637C3×C4—182no—
638C3×C4—181no—
639C3×C4—181no—
640C3×C4—182no—
641C3×C4—181no—
642C3×C4—182no—
643C3×C4D3×Dic612yes—
644C3×C4D3×Dic612yes—
645C3×C4#379712yes—
646Dic3—32no—
647Dic3—32no—
648Dic3—62no—
649Dic3—62no—
650Dic3—61no—
651Dic3—61no—
652Dic3—62no—
653Dic3—62no—
654Dic3—61no—
655Dic3—62no—
656Dic3—62no—
657Dic3—62no—
658Dic3—61no—
659Dic3—61no—
660Dic3—62no—
661Dic3—61no—
662Dic3—122no—
663Dic3—122no—
664Dic3—121no—
665Dic3—122no—
666Dic3—121no—
667C32—21no—
668C32—21no—
669C32—21no—
670C32—41no—
671C32#553911yescharacteristic, complemented
672C32#557911yescharacteristic, complemented
673C32#569011yescharacteristic, complemented
674C23—92no—
675Q8—182no—
676Q8—1082no—
677D4—94no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—91no—
681C2×C4—91no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—92no—
685C2×C4—362no—
686C2×C4—544no—
687C2×C4—1082no—
688C2×C4C2×#111311yescharacteristic
689C2×C4C2×#111311yescharacteristic
690C2×C4C2×#111311yescharacteristic
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3—41no—
703C2×C3—184no—
704C2×C3C2×D3×Dic611yescharacteristic
705C2×C3C2×D3×Dic611yescharacteristic
706C2×C3C2×#379711yescharacteristic
707C2×C3D3×#23511yescharacteristic
708C2×C3D3×#23511yescharacteristic
709C2×C3#6430611yescharacteristic
710C2×C3#6430711yescharacteristic
711C2×C3#6430711yescharacteristic
712C2×C3#6430811yescharacteristic
713D3—64no—
714D3—64no—
715D3—124no—
716C22—94no—
717C22—182no—
718C22—182no—
719C22C22×#111311yescharacteristic
720C4—21no—
721C4—21no—
722C4—92no—
723C4—182no—
724C4—181no—
725C4—182no—
726C4—181no—
727C4—182no—
728C4—181no—
729C4#8904012yes—
730C3—21no—
731C3—21no—
732C3—21no—
733C3—41no—
734C3#1059392911yescharacteristic, complemented
735C3#1059393811yescharacteristic, complemented
736C3#1059394111yescharacteristic, complemented
737C2—184no—
738C2C2×#8904011yescharacteristic
739C2#1172461811yescharacteristic
740C2#1172461911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC42#1113
hypocenterC33#554
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. C4⋊#6296C2semidirect
5. #11723692C2semidirect
8. #11723688C2semidirect
9. #11723682C2semidirect
10. #11723680C2semidirect
11. #11723671C2semidirect
39. #64079D3semidirect
40. C4×#634D3semidirect
85. C3×C4⋊(C3⋊D3)Q8semidirect
263. C4⋊(C3⋊D3)Dic6semidirect
476. C33#554semidirect
671. C32#5539semidirect
672. C32#5579semidirect
673. C32#5690semidirect
734. C3#10593929semidirect
735. C3#10593938semidirect
736. C3#10593941semidirect

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
C4⋊#62962
#117236922
#117236912
#117236882
#117236822
#117236802
#117236712
#105939413
#105939383
#105939293