Finite Group Databasebeta

← C3×#79855 #11897522

Subgroups — C3×#79855 #11897522

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5539C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C32×#442C211yesmaximal, characteristic
4C3×#5152C211yesmaximal, characteristic
5C3×Dic3×D8C211yesmaximal, characteristic
6C3×#5009C211yesmaximal, characteristic, complemented
7C3×#5008C211yesmaximal, characteristic, complemented
8C3×#4856C211yesmaximal, characteristic, complemented
9C3×#4855C211yesmaximal, characteristic, complemented
10C3×#4766C211yesmaximal, characteristic, complemented
11C3×#4761C211yesmaximal, characteristic, complemented
12C3×#4761C211yesmaximal, characteristic, complemented
13C3×#4759C211yesmaximal, characteristic, complemented
14C3×#4702C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3384—31nomaximal
17#79855C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6—21no—
19C2×C32×D8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C3×#924—21no—
27C3×#924—21no—
28C2×C3×Dic3⋊C4—21no—
29C3×#890C2211yescharacteristic
30C3×#888C2211yescharacteristic
31C3×#888C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#878—21no—
34C3×#878—21no—
35C3×#878—21no—
36C3×#878—21no—
37C3×#870C2211yescharacteristic
38C3×#869C2211yescharacteristic
39C3×C4×Dic6C2211yescharacteristic
40C32×#106C2211yescharacteristic
41C32×#102C2211yescharacteristic
42C32×#102C2211yescharacteristic
43C32×#97C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
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×#808C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#554—31no—
62C3×D4×Q8—31no—
63#5539C2×C311yescharacteristic, complemented
64D4×Dic6C2×C311yescharacteristic, complemented
65C3×#501—31no—
66C3×#501—31no—
67C3×#498—31no—
68C3×#478—31no—
69C3×#478—31no—
70C3×#476—31no—
71C3×#476—31no—
72C3×#476—31no—
73C3×#474—31no—
74C3×#446—31no—
75C3×#442—21no—
76C3×#442—31no—
77C3×#442D311yescharacteristic
78C3×#442C2×C311yescharacteristic
79C3×C4×D8—31no—
80#5152C2×C311yescharacteristic
81Dic3×D8C2×C311yescharacteristic
82#5009C2×C311yescharacteristic, complemented
83#5008C2×C311yescharacteristic, complemented
84#4856C2×C311yescharacteristic, complemented
85#4855C2×C311yescharacteristic, complemented
86#4766C2×C311yescharacteristic, complemented
87#4761C2×C311yescharacteristic, complemented
88#4761C2×C311yescharacteristic, complemented
89#4759C2×C311yescharacteristic, complemented
90#4702C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—44no—
105C2×C3×Dic6D411yescharacteristic
106C32×D8Q814yescomplemented
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3384—31noSylow
138C22×C3×Q8—61no—
139C22×Dic6—21no—
140C2×C3×D8—21no—
141C2×C3×D8C2×D311yescharacteristic
142C2×C3×D8C22×C311yescharacteristic
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—31no—
147C3×#125—31no—
148C3×#125—31no—
149C3×C22⋊Q8—61no—
150C3×C22⋊Q8—61no—
151C3×C22⋊Q8—61no—
152C3×C22⋊Q8—61no—
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8—61no—
155C3×C4×Q8—31no—
156C3×C4×D4—21no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4C2×D311yescharacteristic
163C3×C4×D4C2×D311yescharacteristic
164C3×C4×D4C22×C311yescharacteristic
165C3×C4×D4C22×C311yescharacteristic
166C2×C3×C4⋊C4—61no—
167D4×Dic3C22×C311yescharacteristic
168D4×Dic3C22×C311yescharacteristic
169D4×Dic3C22×C311yescharacteristic
170D4×Dic3C22×C311yescharacteristic
171#924—21no—
172#924—21no—
173C2×Dic3⋊C4—21no—
174#890C22×C311yescharacteristic
175#888C22×C311yescharacteristic
176#888C22×C311yescharacteristic
177#888C22×C311yescharacteristic
178#878—21no—
179#878—21no—
180#878—21no—
181#878—21no—
182#870C22×C311yescharacteristic
183#869C22×C311yescharacteristic
184C4×Dic6C22×C311yescharacteristic
185C3×#107—31no—
186C3×#107—31no—
187C3×#107—31no—
188C3×#106—21no—
189C3×#106—31no—
190C3×#106—31no—
191C3×#106—31no—
192C3×#106—31no—
193C3×#106—31no—
194C3×#106C2×D311yescharacteristic
195C3×#106C22×C311yescharacteristic
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8—31no—
199C3×#102—21no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic
206C3×#102C2×D311yescharacteristic
207C3×#102C22×C311yescharacteristic
208C3×#102C22×C311yescharacteristic
209C3×#97—21no—
210C3×#97—31no—
211C3×#97C2×D311yescharacteristic
212C3×#97C22×C311yescharacteristic
213C3×C4×C8—31no—
214#832C22×C311yescharacteristic
215#832C22×C311yescharacteristic
216#832C22×C311yescharacteristic
217#832C22×C311yescharacteristic
218#818C22×C311yescharacteristic
219#818C22×C311yescharacteristic
220#817C22×C311yescharacteristic
221#817C22×C311yescharacteristic
222#815C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226#808C22×C311yescharacteristic
227#808C22×C311yescharacteristic
228#808C22×C311yescharacteristic
229#807C22×C311yescharacteristic
230C4⋊(C3⋊C8)C22×C311yescharacteristic
231C23×C32—21no—
232C23×C32—21no—
233C32×D4—21no—
234C32×D4—21no—
235C32×D4C2×Q812yes—
236C32×D4C2×Q812yescomplemented
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—42no—
240C2×C32×C4—81no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—42no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3—42no—
251C2×C3×Dic3—81no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×Dic6—22no—
257C3×Dic6—42no—
258C3×Dic6—42no—
259C3×Dic6—42no—
260C3×Dic6—81no—
261C32×C8—21no—
262C32×C8C2×Q812yescomplemented
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#554—31no—
266D4×Q8—31no—
267#501—31no—
268#501—31no—
269#498—31no—
270#478—31no—
271#478—31no—
272#476—31no—
273#476—31no—
274#476—31no—
275#474—31no—
276#446—31no—
277#442—31no—
278#442C3×D311yescharacteristic
279C4×D8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8—61no—
283C2×C3×Q8—61no—
284C2×C3×Q8—61no—
285C2×C3×Q8—124no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C22×D311yescharacteristic
290C2×C3×D4C23×C311yescharacteristic
291C2×C3×D4C23×C311yescharacteristic
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—41no—
297C22×C3×C4—41no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—44no—
311C2×Dic6C3×D411yescharacteristic
312C3×D8—24no—
313C3×D8Dic614yescomplemented
314C3×D8C3×Q814yescomplemented
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C22×D311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C2×C3×C8C23×C311yescharacteristic
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C23×C311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—21no—
355C3×C42—31no—
356C3×C42—31no—
357C3×C42C22×D311yescharacteristic
358C3×C42C23×C311yescharacteristic
359#217—21no—
360#217—21no—
361#217—21no—
362#217—21no—
363C4⋊Dic3—21no—
364C4⋊Dic3—21no—
365C4⋊Dic3C3×D411yescharacteristic
366C4⋊Dic3C23×C311yescharacteristic
367C4⋊Dic3C23×C311yescharacteristic
368C4⋊Dic3C23×C311yescharacteristic
369C4⋊Dic3C23×C311yescharacteristic
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4C3×D411yescharacteristic
377Dic3⋊C4C3×D411yescharacteristic
378C4×Dic3C23×C311yescharacteristic
379C4×Dic3C23×C311yescharacteristic
380C2×C3⋊C8C23×C311yescharacteristic
381C2×C3⋊C8C23×C311yescharacteristic
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32C22×D411yescharacteristic
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—41no—
392C32×C4—41no—
393C32×C4C22×Q811yescharacteristic
394C32×C42−1+411yescharacteristic
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3AGL(1,ℤ/8)12yes—
403C22×Q8—61no—
404C2×D8C2×C3×D311yescharacteristic
405C4⋊Q8—31no—
406C4⋊Q8—31no—
407C4⋊Q8—31no—
408C4⋊Q8—31no—
409#125—31no—
410#125—31no—
411C22⋊Q8—61no—
412C22⋊Q8—61no—
413C22⋊Q8—61no—
414C22⋊Q8—61no—
415C22⋊Q8—61no—
416C22⋊Q8—61no—
417C4×Q8—31no—
418C4×D4—31no—
419C4×D4—31no—
420C4×D4—31no—
421C4×D4—31no—
422C4×D4C2×C3×D311yescharacteristic
423C4×D4C2×C3×D311yescharacteristic
424C2×C4⋊C4—61no—
425#107—31no—
426#107—31no—
427#107—31no—
428#106—31no—
429#106—31no—
430#106—31no—
431#106—31no—
432#106—31no—
433#106C2×C3×D311yescharacteristic
434C4⋊C8—31no—
435C4⋊C8—31no—
436C4⋊C8—31no—
437#102—31no—
438#102—31no—
439#102—31no—
440#102—31no—
441#102C2×C3×D311yescharacteristic
442#102C2×C3×D311yescharacteristic
443#97—31no—
444#97C2×C3×D311yescharacteristic
445C4×C8—31no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—41no—
451C23×C3—41no—
452C3×Q8—62no—
453C3×Q8—122no—
454C3×Q8—122no—
455C3×Q8—122no—
456C3×Q8—241no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—22no—
462C3×D4—22no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4C2×Dic612yes—
466C3×D4C2×Dic612yescomplemented
467C3×D4C2×C3×Q812yes—
468C3×D4C2×C3×Q812yescomplemented
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—42no—
483C2×C3×C4—42no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—82no—
489C2×C3×C4—81no—
490C2×C3×C4—81no—
491C2×C3×C4—82no—
492C2×C3×C4—122no—
493C2×C3×C4—122no—
494C2×C3×C4—122no—
495C2×C3×C4—241no—
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4C2×C3×D411yescharacteristic
499C2×C3×C4C2×C3×D411yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C24×C311yescharacteristic
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—42no—
507C2×Dic3—42no—
508C2×Dic3—42no—
509C2×Dic3—81no—
510C2×Dic3C2×C3×D411yescharacteristic
511C2×Dic3C2×C3×D411yescharacteristic
512C2×Dic3C2×C3×D411yescharacteristic
513C2×Dic3C2×C3×D411yescharacteristic
514Dic6—22no—
515Dic6—42no—
516Dic6—42no—
517Dic6—42no—
518Dic6—81no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—22no—
522C3×C8—41no—
523C3×C8—61no—
524C3×C8—61no—
525C3×C8C2×Dic612yescomplemented
526C3×C8C2×C3×Q812yescomplemented
527C3⋊C8—21no—
528C3⋊C8—21no—
529C2×C32—42no—
530C2×C32—42no—
531C2×C32D4×Q811yescharacteristic
532C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
533C2×C32#57711yescharacteristic
534C2×Q8—31no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—124no—
540C2×D4C22×C3×D311yescharacteristic
541C2×D4C22×C3×D311yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548D8C3×Dic614yescomplemented
549C2×C8—31no—
550C2×C8—31no—
551C2×C8C22×C3×D311yescharacteristic
552C2×C8C22×C3×D311yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4C22×C3×D311yescharacteristic
569C4⋊C4C22×C3×D311yescharacteristic
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—61no—
573C22⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C42—31no—
577C42—31no—
578C42C22×C3×D311yescharacteristic
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—21no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3C2×D3×D411yescharacteristic
599C22×C3C22×C3×D411yescharacteristic
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—32no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—81no—
617C3×C4—81no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4—121no—
622C3×C4C22×Dic611yescharacteristic
623C3×C4#101011yescharacteristic
624C3×C4C22×C3×Q811yescharacteristic
625C3×C4C3×2−1+411yescharacteristic
626Dic3—21no—
627Dic3—21no—
628Dic3—21no—
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—41no—
633Dic3C3×AGL(1,ℤ/8)12yes—
634C32#338411yescharacteristic, complemented, Sylow
635C23—21no—
636C23—21no—
637Q8—62no—
638Q8—122no—
639Q8—122no—
640Q8—122no—
641Q8—241no—
642D4—21no—
643D4—21no—
644D4C2×C3×Dic612yes—
645D4C2×C3×Dic612yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—42no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—81no—
658C2×C4—122no—
659C2×C4—122no—
660C2×C4—122no—
661C2×C4—241no—
662C2×C4C3×D3×D411yescharacteristic
663C2×C4C3×D3×D411yescharacteristic
664C2×C4C23×C3×D311yescharacteristic
665C8—21no—
666C8—61no—
667C8—61no—
668C8C2×C3×Dic612yescomplemented
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—42no—
675C2×C3—42no—
676C2×C3—82no—
677C2×C3—82no—
678C2×C3D4×Dic611yescharacteristic
679C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
680C2×C3#577511yescharacteristic
681C2×C3C3×D4×Q811yescharacteristic
682C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
683C2×C3C3×#57711yescharacteristic
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C2×C3×D3×D411yescharacteristic
691C4—21no—
692C4—21no—
693C4—32no—
694C4—41no—
695C4—41no—
696C4—61no—
697C4—61no—
698C4—61no—
699C4—121no—
700C4—121no—
701C4—121no—
702C4—121no—
703C4C22×C3×Dic611yescharacteristic
704C4C3×#101011yescharacteristic
705C3—21no—
706C3#7985511yescharacteristic, direct product factor
707C3C3×#338411yescharacteristic, complemented
708C2—42no—
709C2—42no—
710C2C3×D4×Dic611yescharacteristic
711C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
712C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#442C2
socleC22×C32C22×D4
prime radicalC2×C32×D8C22
hypercenterC3×#442D3
hypocenterC3C3×#3384
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C3×#5539C2semidirect
2. C3×D4×Dic6C2semidirect
6. C3×#5009C2semidirect
7. C3×#5008C2semidirect
8. C3×#4856C2semidirect
9. C3×#4855C2semidirect
10. C3×#4766C2semidirect
11. C3×#4761C2semidirect
12. C3×#4761C2semidirect
13. C3×#4759C2semidirect
14. C3×#4702C2semidirect
15. C3×#4701C2semidirect
17. #79855C3direct (N × H)
63. #5539C2×C3semidirect
64. D4×Dic6C2×C3semidirect
82. #5009C2×C3semidirect
83. #5008C2×C3semidirect
84. #4856C2×C3semidirect
85. #4855C2×C3semidirect
86. #4766C2×C3semidirect
87. #4761C2×C3semidirect
88. #4761C2×C3semidirect
89. #4759C2×C3semidirect
90. #4702C2×C3semidirect
91. #4701C2×C3semidirect
106. C32×D8Q8semidirect
236. C32×D4C2×Q8semidirect
262. C32×C8C2×Q8semidirect
313. C3×D8Dic6semidirect
314. C3×D8C3×Q8semidirect
466. C3×D4C2×Dic6semidirect
468. C3×D4C2×C3×Q8semidirect
525. C3×C8C2×Dic6semidirect
526. C3×C8C2×C3×Q8semidirect
548. D8C3×Dic6semidirect
634. C32#3384semidirect
645. D4C2×C3×Dic6semidirect
668. C8C2×C3×Dic6semidirect
706. C3#79855direct (N × H)
707. C3C3×#3384semidirect

Maximal subgroups

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

subgroupindex
C3×#55392
C3×D4×Dic62
C32×#4422
C3×#51522
C3×Dic3×D82
C3×#50092
C3×#50082
C3×#48562
C3×#48552
C3×#47662
C3×#47612
C3×#47592
C3×#47022
C3×#47012
C3×#33843
#798553