Finite Group Databasebeta

← C3×#81100 #11895833

Subgroups — C3×#81100 #11895833

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic, complemented
2C3×#5568C211yesmaximal, characteristic, complemented
3C32×#477C211yesmaximal, characteristic, complemented
4C3×#5089C211yesmaximal, characteristic, complemented
5C3×#5026C211yesmaximal, characteristic, complemented
6C3×#4890C211yesmaximal, characteristic, complemented
7C3×#4889C211yesmaximal, characteristic, complemented
8C3×#4875C211yesmaximal, characteristic, complemented
9C3×#4872C211yesmaximal, characteristic
10C3×#4844C211yesmaximal, characteristic
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4819C211yesmaximal, characteristic
13C3×#4818C211yesmaximal, characteristic, complemented
14C3×#4794C211yesmaximal, characteristic, complemented
15C3×#4792C211yesmaximal, characteristic, complemented
16C3×#3367—31nomaximal
17#81100C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8—21no—
19C32×C4⋊Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×#946—21no—
23C3×#944C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#898—21no—
28C3×#896—21no—
29C3×#896—21no—
30C3×#896—21no—
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#888C2211yescharacteristic
35C3×#888C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#876—21no—
38C3×#875C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×#872—21no—
41C3×C4×Dic6C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#556—31no—
62C3×D4×Q8—31no—
63#5727C2×C311yescharacteristic, complemented
64#5568C2×C311yescharacteristic, complemented
65C3×#489—31no—
66C3×#489—31no—
67C3×#487—31no—
68C3×#477—21no—
69C3×#477—31no—
70C3×#477D311yescharacteristic, complemented
71C3×#477C2×C311yescharacteristic, complemented
72C3×#474—31no—
73C3×#463—31no—
74C3×#463—31no—
75C3×#461—31no—
76C3×#446—31no—
77C3×#440—31no—
78C3×#440—31no—
79C3×C4×D8—31no—
80#5089C2×C311yescharacteristic, complemented
81#5026C2×C311yescharacteristic, complemented
82#4890C2×C311yescharacteristic, complemented
83#4889C2×C311yescharacteristic, complemented
84#4875C2×C311yescharacteristic, complemented
85#4872C2×C311yescharacteristic
86#4844C2×C311yescharacteristic
87#4828C2×C311yescharacteristic, complemented
88#4819C2×C311yescharacteristic
89#4818C2×C311yescharacteristic, complemented
90#4794C2×C311yescharacteristic, complemented
91#4792C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—44no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114C3×#215—22no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3D411yescharacteristic
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⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×D24—22no—
138C3×#204—22no—
139#3367—31noSylow
140C22×C3×Q8—61no—
141C2×D3×Q8—21no—
142C2×C3×SD16—31no—
143C2×C3×SD16—31no—
144C2×C3×D8—31no—
145C3×C4⋊Q8—21no—
146C3×C4⋊Q8—31no—
147C3×C4⋊Q8—31no—
148C3×C4⋊Q8—31no—
149C3×C4⋊Q8C2×D311yescharacteristic
150C3×C4⋊Q8C22×C311yescharacteristic
151C3×#126—61no—
152C3×#126—61no—
153C3×#124—31no—
154C3×#124—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8C2×D311yescharacteristic
163C3×C4×Q8C22×C311yescharacteristic
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×#117—61no—
169#947C22×C311yescharacteristic
170#946—21no—
171#944C22×C311yescharacteristic
172C2×#215C22×C311yescharacteristic
173C2×D24C22×C311yescharacteristic
174C2×#204C22×C311yescharacteristic
175#898—21no—
176#896—21no—
177#896—21no—
178#896—21no—
179#893C22×C311yescharacteristic
180#893C22×C311yescharacteristic
181#893C22×C311yescharacteristic
182#888C22×C311yescharacteristic
183#888C22×C311yescharacteristic
184#887C22×C311yescharacteristic
185#876—21no—
186#875C22×C311yescharacteristic
187C4×D12C22×C311yescharacteristic
188#872—21no—
189C4×Dic6C22×C311yescharacteristic
190C3×#107—21no—
191C3×#107—21no—
192C3×#107—31no—
193C3×#107C2×D311yescharacteristic
194C3×#107C2×D311yescharacteristic
195C3×#107C22×C311yescharacteristic
196C3×#107C22×C311yescharacteristic
197C3×C4⋊C8—21no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C22×C311yescharacteristic
202C3×#103—21no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C2×D311yescharacteristic
210C3×#103C22×C311yescharacteristic
211C3×#103C22×C311yescharacteristic
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#97—31no—
217C3×#97—31no—
218C3×C4×C8—31no—
219#835C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#816C22×C311yescharacteristic
222#815C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226#810C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232#803C22×C311yescharacteristic
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C32×Q8—42no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—21no—
254C3×D12#4112yes—
255C3×C4×D3—42no—
256C3×C4×D3—42no—
257C3×C4×D3—42no—
258C3×C4×D3—42no—
259C3×Dic6—22no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—42no—
263C3×Dic6—42no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#556—31no—
269D4×Q8—31no—
270#489—31no—
271#489—31no—
272#487—31no—
273#477—31no—
274#477C3×D311yescharacteristic, complemented
275#474—31no—
276#463—31no—
277#463—31no—
278#461—31no—
279#446—31no—
280#440—31no—
281#440—31no—
282C4×D8—31no—
283C2×C3×Q8—21no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—31no—
287C2×C3×Q8—31no—
288C2×C3×Q8—41no—
289C2×C3×Q8—61no—
290C2×C3×Q8—61no—
291C2×C3×Q8—124no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300D3×Q8—44no—
301C2×D12C23×C311yescharacteristic
302C2×D12C23×C311yescharacteristic
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6C3×D411yescharacteristic
310C2×Dic6C23×C311yescharacteristic
311C3×SD16—62no—
312C3×SD16—62no—
313C3×D8—62no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C23×C311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4—41no—
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⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C4⋊C4C23×C311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—41no—
360C3×C42—61no—
361C3×C42C22×D311yescharacteristic
362C3×C42C23×C311yescharacteristic
363#215—22no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372C4⋊Dic3C3×D411yescharacteristic
373C4⋊Dic3C23×C311yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4C3×D411yescharacteristic
380Dic3⋊C4C3×D411yescharacteristic
381C4×Dic3—21no—
382C4×Dic3C23×C311yescharacteristic
383C4×Dic3C23×C311yescharacteristic
384C2×C3⋊C8C23×C311yescharacteristic
385C2×C3⋊C8C23×C311yescharacteristic
386D24—22no—
387#204—22no—
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—22no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C42−1+411yescharacteristic
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3AGL(1,ℤ/8)12yes—
409C22×Q8—61no—
410C2×SD16—31no—
411C2×SD16—31no—
412C2×D8—31no—
413C4⋊Q8—31no—
414C4⋊Q8—31no—
415C4⋊Q8—31no—
416C4⋊Q8C2×C3×D311yescharacteristic
417#126—61no—
418#126—61no—
419#124—31no—
420#124—31no—
421C22⋊Q8—61no—
422C22⋊Q8—61no—
423C22⋊Q8—61no—
424C22⋊Q8—61no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8C2×C3×D311yescharacteristic
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—31no—
431C4×D4—31no—
432#117—61no—
433#107—31no—
434#107C2×C3×D311yescharacteristic
435#107C2×C3×D311yescharacteristic
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8C2×C3×D311yescharacteristic
439#103—31no—
440#103—31no—
441#103—31no—
442#103—31no—
443#103C2×C3×D311yescharacteristic
444#103C2×C3×D311yescharacteristic
445#102—31no—
446#102—31no—
447#102—31no—
448#102—31no—
449#97—31no—
450#97—31no—
451C4×C8—31no—
452C23×C3—61no—
453C23×C3—61no—
454C22×D3—21no—
455C22×D3—21no—
456C3×Q8—22no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—41no—
462C3×Q8—42no—
463C3×Q8—42no—
464C3×Q8—62no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—82no—
468C3×Q8—122no—
469C3×Q8—122no—
470C3×D4—32no—
471C3×D4—61no—
472C3×D4—61no—
473C3×D4—61no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—122no—
496C2×C3×C4—122no—
497C2×C3×C4—122no—
498C2×C3×C4—122no—
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4C2×C3×D411yescharacteristic
502C2×C3×C4C2×C3×D411yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C24×C311yescharacteristic
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3C2×C3×D411yescharacteristic
508C2×Dic3C2×C3×D411yescharacteristic
509C2×Dic3C2×C3×D411yescharacteristic
510C2×Dic3C2×C3×D411yescharacteristic
511D12—21no—
512D12—21no—
513D12—21no—
514D12C3×#4112yes—
515C4×D3—42no—
516C4×D3—42no—
517C4×D3—42no—
518C4×D3—42no—
519Dic6—22no—
520Dic6—21no—
521Dic6—21no—
522Dic6—42no—
523Dic6—42no—
524C3×C8—21no—
525C3×C8—21no—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—41no—
529C3×C8—41no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C2×C32#54811yescharacteristic
535C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
536C2×C32#57811yescharacteristic
537C3×D3—42no—
538C3×D3—81no—
539C2×Q8—21no—
540C2×Q8—31no—
541C2×Q8—31no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×Q8—124no—
545C2×Q8C22×C3×D311yescharacteristic
546C2×D4—31no—
547C2×D4—31no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552SD16—62no—
553SD16—62no—
554D8—62no—
555C2×C8—31no—
556C2×C8—31no—
557C2×C8C22×C3×D311yescharacteristic
558C2×C8C22×C3×D311yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4C22×C3×D311yescharacteristic
571C4⋊C4C22×C3×D311yescharacteristic
572C4⋊C4C22×C3×D311yescharacteristic
573C22⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C42—21no—
582C42—31no—
583C42—31no—
584C42—61no—
585C42C22×C3×D311yescharacteristic
586C22×C3—21no—
587C22×C3—62no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C22×C3×D411yescharacteristic
595C2×D3—22no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C3×C4—22no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—32no—
609C3×C4—41no—
610C3×C4—42no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—61no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—81no—
623C3×C4—81no—
624C3×C4—81no—
625C3×C4—121no—
626C3×C4—121no—
627C3×C4#100711yescharacteristic
628C3×C4D3×#4111yescharacteristic
629C3×C4C2×C3×#4111yescharacteristic
630C3×C4C3×2−1+411yescharacteristic
631Dic3—21no—
632Dic3—21no—
633Dic3—21no—
634Dic3—41no—
635Dic3—41no—
636Dic3C3×AGL(1,ℤ/8)12yes—
637C32#336711yescharacteristic, complemented, Sylow
638C23—61no—
639C23—61no—
640Q8—21no—
641Q8—21no—
642Q8—42no—
643Q8—62no—
644Q8—61no—
645Q8—61no—
646Q8—122no—
647Q8—122no—
648D4—32no—
649D4—61no—
650D4—61no—
651D4—61no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—122no—
663C2×C4—122no—
664C2×C4—122no—
665C2×C4—122no—
666C2×C4C3×D3×D411yescharacteristic
667C2×C4C3×D3×D411yescharacteristic
668C2×C4C23×C3×D311yescharacteristic
669C8—21no—
670C8—21no—
671C8—61no—
672C8—61no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—122no—
677C2×C3—241no—
678C2×C3#563311yescharacteristic
679C2×C3#576611yescharacteristic
680C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
681C2×C3C3×#54811yescharacteristic
682C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
683C2×C3C3×#57811yescharacteristic
684D3—42no—
685D3—81no—
686C22—62no—
687C22—121no—
688C22—121no—
689C22—121no—
690C22—121no—
691C22—121no—
692C22C2×C3×D3×D411yescharacteristic
693C4—21no—
694C4—21no—
695C4—32no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—61no—
701C4—61no—
702C4—61no—
703C4—121no—
704C4—121no—
705C4C3×#100711yescharacteristic
706C4C3×D3×#4111yescharacteristic
707C3—21no—
708C3#8110011yescharacteristic, direct product factor
709C3C3×#336711yescharacteristic, complemented
710C2—122no—
711C2—241no—
712C2C3×#563311yescharacteristic
713C2C3×#576611yescharacteristic
714C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC3×#477D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
1. C3×#5727C2semidirect
2. C3×#5568C2semidirect
3. C32×#477C2semidirect
4. C3×#5089C2semidirect
5. C3×#5026C2semidirect
6. C3×#4890C2semidirect
7. C3×#4889C2semidirect
8. C3×#4875C2semidirect
11. C3×#4828C2semidirect
13. C3×#4818C2semidirect
14. C3×#4794C2semidirect
15. C3×#4792C2semidirect
17. #81100C3direct (N × H)
63. #5727C2×C3semidirect
64. #5568C2×C3semidirect
70. C3×#477D3semidirect
71. C3×#477C2×C3semidirect
80. #5089C2×C3semidirect
81. #5026C2×C3semidirect
82. #4890C2×C3semidirect
83. #4889C2×C3semidirect
84. #4875C2×C3semidirect
87. #4828C2×C3semidirect
89. #4818C2×C3semidirect
90. #4794C2×C3semidirect
91. #4792C2×C3semidirect
274. #477C3×D3semidirect
637. C32#3367semidirect
708. C3#81100direct (N × H)
709. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#55682
C32×#4772
C3×#50892
C3×#50262
C3×#48902
C3×#48892
C3×#48752
C3×#48722
C3×#48442
C3×#48282
C3×#48192
C3×#48182
C3×#47942
C3×#47922
C3×#33673
#811003