Finite Group Databasebeta

← C3×#79759 #11897624

Subgroups — C3×#79759 #11897624

Order 1152.

740 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2C3×#5539C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic
4C3×#5164C211yesmaximal, characteristic
5C3×Dic3×SD16C211yesmaximal, characteristic
6C3×#5022C211yesmaximal, characteristic, complemented
7C3×#5007C211yesmaximal, characteristic
8C3×#4876C211yesmaximal, characteristic, complemented
9C3×#4874C211yesmaximal, characteristic, complemented
10C3×#4799C211yesmaximal, characteristic, complemented
11C3×#4793C211yesmaximal, characteristic, complemented
12C3×#4761C211yesmaximal, characteristic
13C3×#4759C211yesmaximal, characteristic
14C3×#4702C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3385—31nomaximal
17#79759C311yesmaximal, characteristic, direct product factor
18C2×C32×SD16C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×#924—21no—
26C2×C3×Dic3⋊C4—21no—
27C3×#890C2211yescharacteristic
28C3×#888—21no—
29C3×#888—21no—
30C3×#888C2211yescharacteristic
31C3×#888C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#878—21no—
34C3×#878—21no—
35C3×#870C2211yescharacteristic
36C3×#869—21no—
37C3×#869C2211yescharacteristic
38C3×C4×Dic6—21no—
39C3×C4×Dic6C2211yescharacteristic
40C32×#107C2211yescharacteristic
41C32×#103C2211yescharacteristic
42C32×#102C2211yescharacteristic
43C32×#97C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#807C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×Q82—31no—
62C3×#554—31no—
63Q8×Dic6C2×C311yescharacteristic, complemented
64#5539C2×C311yescharacteristic
65C3×#501—31no—
66C3×#501—31no—
67C3×#500—31no—
68C3×#479—31no—
69C3×#479—31no—
70C3×#477—31no—
71C3×#476—31no—
72C3×#474—31no—
73C3×#474—31no—
74C3×#446—31no—
75C3×#440—21no—
76C3×#440—31no—
77C3×#440D311yescharacteristic
78C3×#440C2×C311yescharacteristic
79C3×C4×SD16—31no—
80#5164C2×C311yescharacteristic
81Dic3×SD16C2×C311yescharacteristic
82#5022C2×C311yescharacteristic, complemented
83#5007C2×C311yescharacteristic
84#4876C2×C311yescharacteristic, complemented
85#4874C2×C311yescharacteristic, complemented
86#4799C2×C311yescharacteristic, complemented
87#4793C2×C311yescharacteristic, complemented
88#4761C2×C311yescharacteristic
89#4759C2×C311yescharacteristic
90#4702C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6D411yescharacteristic
102C32×SD16Q814yescomplemented
103C2×C32×C8C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3385—31noSylow
137C2×C3×SD16—21no—
138C2×C3×SD16C2×D311yescharacteristic
139C2×C3×SD16C22×C311yescharacteristic
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—61no—
145C3×C4⋊Q8—61no—
146C3×C4⋊Q8—61no—
147C3×#125—31no—
148C3×#125—31no—
149C3×C22⋊Q8—61no—
150C3×C22⋊Q8—61no—
151C3×C22⋊Q8—61no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—61no—
157C3×C4×Q8C2×D311yescharacteristic
158C3×C4×Q8C22×C311yescharacteristic
159C3×C4×D4—21no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4C2×D311yescharacteristic
163C3×C4×D4C22×C311yescharacteristic
164C2×C3×C4⋊C4—61no—
165Q8×Dic3C22×C311yescharacteristic
166Q8×Dic3C22×C311yescharacteristic
167D4×Dic3C22×C311yescharacteristic
168D4×Dic3C22×C311yescharacteristic
169#924—21no—
170C2×Dic3⋊C4—21no—
171#890C22×C311yescharacteristic
172#888—21no—
173#888—21no—
174#888C22×C311yescharacteristic
175#888C22×C311yescharacteristic
176#888C22×C311yescharacteristic
177#878—21no—
178#878—21no—
179#870C22×C311yescharacteristic
180#869—21no—
181#869C22×C311yescharacteristic
182C4×Dic6—21no—
183C4×Dic6C22×C311yescharacteristic
184C3×#107—21no—
185C3×#107—31no—
186C3×#107—31no—
187C3×#107—31no—
188C3×#107—31no—
189C3×#107—31no—
190C3×#107C2×D311yescharacteristic
191C3×#107C22×C311yescharacteristic
192C3×#106—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#103—21no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103C2×D311yescharacteristic
202C3×#103C22×C311yescharacteristic
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C22×C311yescharacteristic
208C3×#97—21no—
209C3×#97—31no—
210C3×#97C2×D311yescharacteristic
211C3×#97C22×C311yescharacteristic
212C3×C4×C8—31no—
213#835C22×C311yescharacteristic
214#835C22×C311yescharacteristic
215#832C22×C311yescharacteristic
216#832C22×C311yescharacteristic
217#818C22×C311yescharacteristic
218#818C22×C311yescharacteristic
219#817C22×C311yescharacteristic
220#817C22×C311yescharacteristic
221#815C22×C311yescharacteristic
222Dic3⋊C8C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224C8×Dic3C22×C311yescharacteristic
225#808C22×C311yescharacteristic
226#807C22×C311yescharacteristic
227#807C22×C311yescharacteristic
228#807C22×C311yescharacteristic
229C4⋊(C3⋊C8)C22×C311yescharacteristic
230C23×C32—21no—
231C32×Q8—21no—
232C32×Q8C2×Q812yes—
233C32×D4—21no—
234C32×D4C2×Q812yes—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—81no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—42no—
247C2×C3×Dic3—81no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×Dic6—22no—
253C3×Dic6—81no—
254C3×Dic6—81no—
255C3×Dic6—81no—
256C3×Dic6—81no—
257C32×C8—21no—
258C32×C8C2×Q812yes—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
261Q82—31no—
262#554—31no—
263#501—31no—
264#501—31no—
265#500—31no—
266#479—31no—
267#479—31no—
268#477—31no—
269#476—31no—
270#474—31no—
271#474—31no—
272#446—31no—
273#440—31no—
274#440C3×D311yescharacteristic
275C4×SD16—31no—
276C2×C3×Q8—21no—
277C2×C3×Q8—31no—
278C2×C3×Q8—61no—
279C2×C3×Q8—61no—
280C2×C3×Q8—61no—
281C2×C3×Q8—61no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C23×C311yescharacteristic
284C2×C3×D4—21no—
285C2×C3×D4C22×D311yescharacteristic
286C2×C3×D4C23×C311yescharacteristic
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—41no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6C3×D411yescharacteristic
299C3×SD16—24no—
300C3×SD16Dic614yescomplemented
301C3×SD16C3×Q814yescomplemented
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C23×C311yescharacteristic
309C2×C3×C8C23×C311yescharacteristic
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—41no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C23×C311yescharacteristic
335C3×C4⋊C4C23×C311yescharacteristic
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—41no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—41no—
347C3×C42—61no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C23×C311yescharacteristic
351#217—21no—
352#217—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3—21no—
357C4⋊Dic3C3×D411yescharacteristic
358C4⋊Dic3C23×C311yescharacteristic
359C4⋊Dic3C23×C311yescharacteristic
360C4⋊Dic3C23×C311yescharacteristic
361C4⋊Dic3C23×C311yescharacteristic
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4C3×D411yescharacteristic
369Dic3⋊C4C3×D411yescharacteristic
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3C23×C311yescharacteristic
373C4×Dic3C23×C311yescharacteristic
374C2×C3⋊C8C23×C311yescharacteristic
375C2×C3⋊C8C23×C311yescharacteristic
376C22×C32—22no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32C22×D411yescharacteristic
380C32×C4—22no—
381C32×C4—21no—
382C32×C4—21no—
383C32×C4—41no—
384C32×C4—41no—
385C32×C4C22×Q811yescharacteristic
386C32×C42−1+411yescharacteristic
387C3×Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3#13712yes—
395C2×SD16C2×C3×D311yescharacteristic
396C4⋊Q8—31no—
397C4⋊Q8—31no—
398C4⋊Q8—31no—
399C4⋊Q8—31no—
400C4⋊Q8—61no—
401C4⋊Q8—61no—
402C4⋊Q8—61no—
403#125—31no—
404#125—31no—
405C22⋊Q8—61no—
406C22⋊Q8—61no—
407C22⋊Q8—61no—
408C4×Q8—31no—
409C4×Q8—31no—
410C4×Q8—31no—
411C4×Q8—61no—
412C4×Q8C2×C3×D311yescharacteristic
413C4×D4—31no—
414C4×D4—31no—
415C4×D4C2×C3×D311yescharacteristic
416C2×C4⋊C4—61no—
417#107—31no—
418#107—31no—
419#107—31no—
420#107—31no—
421#107—31no—
422#107C2×C3×D311yescharacteristic
423#106—31no—
424#106—31no—
425#106—31no—
426C4⋊C8—31no—
427C4⋊C8—31no—
428C4⋊C8—31no—
429#103—31no—
430#103—31no—
431#103C2×C3×D311yescharacteristic
432#102—31no—
433#102—31no—
434#102C2×C3×D311yescharacteristic
435#97—31no—
436#97C2×C3×D311yescharacteristic
437C4×C8—31no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—41no—
441C3×Q8—21no—
442C3×Q8—21no—
443C3×Q8—22no—
444C3×Q8—41no—
445C3×Q8—62no—
446C3×Q8—241no—
447C3×Q8—241no—
448C3×Q8—241no—
449C3×Q8—241no—
450C3×Q8C2×Dic612yes—
451C3×Q8C2×C3×Q812yes—
452C3×D4—21no—
453C3×D4—21no—
454C3×D4—22no—
455C3×D4—41no—
456C3×D4C2×Dic612yes—
457C3×D4C2×C3×Q812yes—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—81no—
479C2×C3×C4—81no—
480C2×C3×C4—82no—
481C2×C3×C4—122no—
482C2×C3×C4—241no—
483C2×C3×C4D3×D411yescharacteristic
484C2×C3×C4D3×D411yescharacteristic
485C2×C3×C4C2×C3×D411yescharacteristic
486C2×C3×C4C2×C3×D411yescharacteristic
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C24×C311yescharacteristic
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—42no—
494C2×Dic3—81no—
495C2×Dic3C2×C3×D411yescharacteristic
496C2×Dic3C2×C3×D411yescharacteristic
497C2×Dic3C2×C3×D411yescharacteristic
498C2×Dic3C2×C3×D411yescharacteristic
499Dic6—22no—
500Dic6—81no—
501Dic6—81no—
502Dic6—81no—
503Dic6—81no—
504C3×C8—21no—
505C3×C8—21no—
506C3×C8—22no—
507C3×C8—41no—
508C3×C8—61no—
509C3×C8—61no—
510C3×C8C2×Dic612yes—
511C3×C8C2×C3×Q812yes—
512C3⋊C8—21no—
513C3⋊C8—21no—
514C2×C32—42no—
515C2×C32D4×Q811yescharacteristic
516C2×C32C2×#13711yescharacteristic
517C2×C32#57611yescharacteristic
518C2×Q8—31no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—61no—
522C2×Q8—61no—
523C2×Q8C22×C3×D311yescharacteristic
524C2×D4C22×C3×D311yescharacteristic
525C22×C4—21no—
526C22×C4—61no—
527C22×C4—61no—
528SD16C3×Dic614yescomplemented
529C2×C8—31no—
530C2×C8—31no—
531C2×C8C22×C3×D311yescharacteristic
532C2×C8C22×C3×D311yescharacteristic
533C4⋊C4—21no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4C22×C3×D311yescharacteristic
552C4⋊C4C22×C3×D311yescharacteristic
553C22⋊C4—21no—
554C22⋊C4—61no—
555C22⋊C4—61no—
556C42—21no—
557C42—31no—
558C42—31no—
559C42—61no—
560C42—61no—
561C42C22×C3×D311yescharacteristic
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—21no—
565C22×C3—42no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C22×C3×D411yescharacteristic
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—22no—
579C3×C4—22no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—32no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—42no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—61no—
591C3×C4—61no—
592C3×C4—61no—
593C3×C4—81no—
594C3×C4—81no—
595C3×C4—121no—
596C3×C4—121no—
597C3×C4—121no—
598C3×C4—121no—
599C3×C4C22×Dic611yescharacteristic
600C3×C4#101011yescharacteristic
601C3×C4C22×C3×Q811yescharacteristic
602C3×C4C3×2−1+411yescharacteristic
603Dic3—21no—
604Dic3—21no—
605Dic3—21no—
606Dic3—41no—
607Dic3—41no—
608Dic3—41no—
609Dic3—41no—
610Dic3C3×#13712yes—
611C32#338511yescharacteristic, complemented, Sylow
612C23—21no—
613Q8—21no—
614Q8—62no—
615Q8—241no—
616Q8—241no—
617Q8—241no—
618Q8—241no—
619Q8C2×C3×Dic612yes—
620D4—21no—
621D4C2×C3×Dic612yes—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—81no—
634C2×C4—122no—
635C2×C4—241no—
636C2×C4C3×D3×D411yescharacteristic
637C2×C4C3×D3×D411yescharacteristic
638C2×C4C23×C3×D311yescharacteristic
639C8—21no—
640C8—61no—
641C8—61no—
642C8C2×C3×Dic612yes—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—82no—
649C2×C3D4×Dic611yescharacteristic
650C2×C3#577411yescharacteristic
651C2×C3D3×#13711yescharacteristic
652C2×C3C3×D4×Q811yescharacteristic
653C2×C3C2×C3×#13711yescharacteristic
654C2×C3C3×#57611yescharacteristic
655C22—22no—
656C22—41no—
657C22—41no—
658C22C2×C3×D3×D411yescharacteristic
659C4—21no—
660C4—21no—
661C4—22no—
662C4—32no—
663C4—41no—
664C4—41no—
665C4—61no—
666C4—61no—
667C4—61no—
668C4—121no—
669C4—121no—
670C4—121no—
671C4—121no—
672C4C22×C3×Dic611yescharacteristic
673C4C3×#101011yescharacteristic
674C3—21no—
675C3#7975911yescharacteristic, direct product factor
676C3C3×#338511yescharacteristic, complemented
677C2—42no—
678C2C3×D4×Dic611yescharacteristic
679C2C3×#577411yescharacteristic
680C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#440D3
hypocenterC3C3×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C3×Q8×Dic6C2semidirect
6. C3×#5022C2semidirect
8. C3×#4876C2semidirect
9. C3×#4874C2semidirect
10. C3×#4799C2semidirect
11. C3×#4793C2semidirect
14. C3×#4702C2semidirect
15. C3×#4701C2semidirect
17. #79759C3direct (N × H)
63. Q8×Dic6C2×C3semidirect
82. #5022C2×C3semidirect
84. #4876C2×C3semidirect
85. #4874C2×C3semidirect
86. #4799C2×C3semidirect
87. #4793C2×C3semidirect
90. #4702C2×C3semidirect
91. #4701C2×C3semidirect
102. C32×SD16Q8semidirect
300. C3×SD16Dic6semidirect
301. C3×SD16C3×Q8semidirect
528. SD16C3×Dic6semidirect
611. C32#3385semidirect
675. C3#79759direct (N × H)
676. C3C3×#3385semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
C3×#55392
C32×#4402
C3×#51642
C3×Dic3×SD162
C3×#50222
C3×#50072
C3×#48762
C3×#48742
C3×#47992
C3×#47932
C3×#47612
C3×#47592
C3×#47022
C3×#47012
C3×#33853
#797593