Finite Group Databasebeta

← C3×#81158 #11897528

Subgroups — C3×#81158 #11897528

Order 1152.

799 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5690C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5064C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic
6C3×#4890C211yesmaximal, characteristic, complemented
7C3×#4876C211yesmaximal, characteristic, complemented
8C3×#4870C211yesmaximal, characteristic, complemented
9C3×#4855C211yesmaximal, characteristic, complemented
10C3×#4842C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic
13C3×#4763C211yesmaximal, characteristic, complemented
14C3×#4761C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic
16C3×#3384—31nomaximal
17#81158C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6—21no—
19C32×#125C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×#924—21no—
25C3×#897—21no—
26C3×#896—21no—
27C3×#896—21no—
28C3×#893C2211yescharacteristic
29C3×#893C2211yescharacteristic
30C3×D3×C4⋊C4—21no—
31C3×#890C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#888C2211yescharacteristic
35C3×#878—21no—
36C3×#878—21no—
37C3×C4×D12C2211yescharacteristic
38C3×#869C2211yescharacteristic
39C3×C4×Dic6C2211yescharacteristic
40C32×#107C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#808C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#808C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#554—31no—
62C3×D4×Q8—31no—
63#5690C2×C311yescharacteristic, complemented
64D4×Dic6C2×C311yescharacteristic, complemented
65C3×#501—31no—
66C3×#501—31no—
67C3×#498—31no—
68C3×#478—21no—
69C3×#478—31no—
70C3×#478D311yescharacteristic, complemented
71C3×#478C2×C311yescharacteristic, complemented
72C3×#476—31no—
73C3×#476—31no—
74C3×#476—31no—
75C3×#474—31no—
76C3×#446—31no—
77C3×#442—31no—
78C3×#442—31no—
79C3×C4×D8—31no—
80#5064C2×C311yescharacteristic, complemented
81#5014C2×C311yescharacteristic
82#4890C2×C311yescharacteristic, complemented
83#4876C2×C311yescharacteristic, complemented
84#4870C2×C311yescharacteristic, complemented
85#4855C2×C311yescharacteristic, complemented
86#4842C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4785C2×C311yescharacteristic
89#4763C2×C311yescharacteristic, complemented
90#4761C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—44no—
105C2×C3×Dic6D411yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#213Q814yescomplemented
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
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—31no—
141C3×C4⋊Q8—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—31no—
145C3×#125—21no—
146C3×#125—31no—
147C3×#125C2×D311yescharacteristic
148C3×#125C22×C311yescharacteristic
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—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4C2×D311yescharacteristic
163C3×C4×D4C22×C311yescharacteristic
164C2×C3×C4⋊C4—61no—
165D4×Dic3C22×C311yescharacteristic
166D4×Dic3C22×C311yescharacteristic
167C2×#213C22×C311yescharacteristic
168#924—21no—
169#897—21no—
170#896—21no—
171#896—21no—
172#893C22×C311yescharacteristic
173#893C22×C311yescharacteristic
174D3×C4⋊C4—21no—
175#890C22×C311yescharacteristic
176#888C22×C311yescharacteristic
177#888C22×C311yescharacteristic
178#888C22×C311yescharacteristic
179#878—21no—
180#878—21no—
181C4×D12C22×C311yescharacteristic
182#869C22×C311yescharacteristic
183C4×Dic6C22×C311yescharacteristic
184C3×#107—21no—
185C3×#107—31no—
186C3×#107—31no—
187C3×#107C2×D311yescharacteristic
188C3×#107C22×C311yescharacteristic
189C3×#106—21no—
190C3×#106—31no—
191C3×#106—31no—
192C3×#106—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#106C2×D311yescharacteristic
196C3×#106C22×C311yescharacteristic
197C3×C4⋊C8—21no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C22×C311yescharacteristic
202C3×#102—21no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×#102C22×C311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#97—31no—
213C3×#97—31no—
214C3×C4×C8—31no—
215#832C22×C311yescharacteristic
216#821C22×C311yescharacteristic
217#821C22×C311yescharacteristic
218#817C22×C311yescharacteristic
219#817C22×C311yescharacteristic
220#815C22×C311yescharacteristic
221Dic3⋊C8C22×C311yescharacteristic
222Dic3⋊C8C22×C311yescharacteristic
223C8×Dic3C22×C311yescharacteristic
224#809C22×C311yescharacteristic
225#808C22×C311yescharacteristic
226#808C22×C311yescharacteristic
227#808C22×C311yescharacteristic
228#807C22×C311yescharacteristic
229#807C22×C311yescharacteristic
230#803C22×C311yescharacteristic
231C23×C32—21no—
232C22×C3×D3—21no—
233C32×D4—21no—
234C32×D4C2×Q812yes—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—42no—
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—42no—
246C2×C3×Dic3—42no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12C2×Q812yescomplemented
253C3×C4×D3—42no—
254C3×C4×D3—81no—
255C3×C4×D3—81no—
256C3×Dic6—22no—
257C3×Dic6—42no—
258C3×Dic6—42no—
259C3×Dic6—42no—
260C3×Dic6—81no—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8C2×Q812yescomplemented
265#554—31no—
266D4×Q8—31no—
267#501—31no—
268#501—31no—
269#498—31no—
270#478—31no—
271#478C3×D311yescharacteristic, complemented
272#476—31no—
273#476—31no—
274#476—31no—
275#474—31no—
276#446—31no—
277#442—31no—
278#442—31no—
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—31no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C23×C311yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—41no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C2×D12C23×C311yescharacteristic
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—44no—
309C2×Dic6C3×D411yescharacteristic
310C3×D8—34no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C23×C311yescharacteristic
318C2×C3×C8C23×C311yescharacteristic
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
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—41no—
333C3×C4⋊C4—41no—
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⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C4⋊C4C23×C311yescharacteristic
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—41no—
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—31no—
356C3×C42—31no—
357C3×C42C22×D311yescharacteristic
358C3×C42C23×C311yescharacteristic
359#217—21no—
360#217—21no—
361#213C3×Q814yescomplemented
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3C3×D411yescharacteristic
368C4⋊Dic3C23×C311yescharacteristic
369C4⋊Dic3C23×C311yescharacteristic
370C4⋊Dic3C23×C311yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4C3×D411yescharacteristic
376Dic3⋊C4C3×D411yescharacteristic
377C4×Dic3C23×C311yescharacteristic
378C4×Dic3C23×C311yescharacteristic
379C2×C3⋊C8C23×C311yescharacteristic
380C2×C3⋊C8C23×C311yescharacteristic
381C22×C32—22no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32C22×D411yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—41no—
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×Dic3AGL(1,ℤ/8)12yes—
402C22×Q8—61no—
403C2×D8—31no—
404C4⋊Q8—31no—
405C4⋊Q8—31no—
406C4⋊Q8—31no—
407C4⋊Q8—31no—
408#125—31no—
409#125C2×C3×D311yescharacteristic
410C22⋊Q8—61no—
411C22⋊Q8—61no—
412C22⋊Q8—61no—
413C22⋊Q8—61no—
414C22⋊Q8—61no—
415C22⋊Q8—61no—
416C4×Q8—31no—
417C4×D4—31no—
418C4×D4—31no—
419C4×D4—31no—
420C4×D4—31no—
421C4×D4—31no—
422C4×D4C2×C3×D311yescharacteristic
423C2×C4⋊C4—61no—
424#107—31no—
425#107—31no—
426#107C2×C3×D311yescharacteristic
427#106—31no—
428#106—31no—
429#106—31no—
430#106—31no—
431#106—31no—
432#106C2×C3×D311yescharacteristic
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8C2×C3×D311yescharacteristic
436#102—31no—
437#102—31no—
438#102—31no—
439#102—31no—
440#102C2×C3×D311yescharacteristic
441#102C2×C3×D311yescharacteristic
442#97—31no—
443#97—31no—
444C4×C8—31no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—41no—
448C23×C3—61no—
449C22×D3—21no—
450C3×Q8—62no—
451C3×Q8—122no—
452C3×Q8—122no—
453C3×Q8—122no—
454C3×Q8—241no—
455C3×D4—21no—
456C3×D4—21no—
457C3×D4—22no—
458C3×D4—32no—
459C3×D4—41no—
460C3×D4—61no—
461C3×D4D3×Q812yes—
462C3×D4C2×C3×Q812yes—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—42no—
480C2×C3×C4—42no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—82no—
485C2×C3×C4—122no—
486C2×C3×C4—122no—
487C2×C3×C4—122no—
488C2×C3×C4—241no—
489C2×C3×C4—241no—
490C2×C3×C4D3×D411yescharacteristic
491C2×C3×C4D3×D411yescharacteristic
492C2×C3×C4C2×C3×D411yescharacteristic
493C2×C3×C4C2×C3×D411yescharacteristic
494C2×C3×C4C23×D311yescharacteristic
495C2×C3×C4C24×C311yescharacteristic
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3C2×C3×D411yescharacteristic
502C2×Dic3C2×C3×D411yescharacteristic
503C2×Dic3C2×C3×D411yescharacteristic
504C2×Dic3C2×C3×D411yescharacteristic
505D12—21no—
506D12C2×C3×Q812yescomplemented
507C4×D3—42no—
508C4×D3—81no—
509C4×D3—81no—
510Dic6—22no—
511Dic6—42no—
512Dic6—42no—
513Dic6—42no—
514Dic6—81no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—32no—
520C3×C8—41no—
521C3×C8—41no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8C2×C3×Q812yescomplemented
525C2×C32—42no—
526C2×C32D4×Q811yescharacteristic
527C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
528C2×C32#57711yescharacteristic
529C3×D3—42no—
530C2×Q8—31no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—124no—
536C2×D4—31no—
537C2×D4C22×C3×D311yescharacteristic
538C22×C4—21no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544D8—34no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8C22×C3×D311yescharacteristic
548C2×C8C22×C3×D311yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4C22×C3×D311yescharacteristic
564C4⋊C4C22×C3×D311yescharacteristic
565C4⋊C4C22×C3×D311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C42—31no—
573C42—31no—
574C42C22×C3×D311yescharacteristic
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—21no—
578C22×C3—42no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—62no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—121no—
587C22×C3—121no—
588C22×C3C2×D3×D411yescharacteristic
589C22×C3C22×C3×D411yescharacteristic
590C2×D3—22no—
591C2×D3—41no—
592C2×D3—41no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—32no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—81no—
612C3×C4—81no—
613C3×C4—81no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4C2×D3×Q811yescharacteristic
618C3×C4#101011yescharacteristic
619C3×C4C22×C3×Q811yescharacteristic
620C3×C4C3×2−1+411yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—41no—
625Dic3—41no—
626Dic3—41no—
627Dic3C3×AGL(1,ℤ/8)12yes—
628C32#338411yescharacteristic, complemented, Sylow
629C23—21no—
630C23—61no—
631Q8—62no—
632Q8—122no—
633Q8—122no—
634Q8—122no—
635Q8—241no—
636D4—21no—
637D4—32no—
638D4—61no—
639D4C3×D3×Q812yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—42no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—122no—
652C2×C4—122no—
653C2×C4—122no—
654C2×C4—241no—
655C2×C4—241no—
656C2×C4C3×D3×D411yescharacteristic
657C2×C4C3×D3×D411yescharacteristic
658C2×C4C23×C3×D311yescharacteristic
659C8—21no—
660C8—21no—
661C8—32no—
662C8—61no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—42no—
667C2×C3—42no—
668C2×C3—82no—
669C2×C3—122no—
670C2×C3#563211yescharacteristic
671C2×C3#577011yescharacteristic
672C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
673C2×C3C3×D4×Q811yescharacteristic
674C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
675C2×C3C3×#57711yescharacteristic
676D3—42no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—62no—
681C22—121no—
682C22—121no—
683C22C2×C3×D3×D411yescharacteristic
684C4—21no—
685C4—21no—
686C4—32no—
687C4—41no—
688C4—41no—
689C4—41no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—121no—
694C4—121no—
695C4—121no—
696C4C2×C3×D3×Q811yescharacteristic
697C4C3×#101011yescharacteristic
698C3—21no—
699C3#8115811yescharacteristic, direct product factor
700C3C3×#338411yescharacteristic, complemented
701C2—42no—
702C2—122no—
703C2C3×#563211yescharacteristic
704C2C3×#577011yescharacteristic
705C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#478D3
hypocenterC3C3×#3384
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5690C2semidirect
2. C3×D4×Dic6C2semidirect
3. C32×#478C2semidirect
4. C3×#5064C2semidirect
6. C3×#4890C2semidirect
7. C3×#4876C2semidirect
8. C3×#4870C2semidirect
9. C3×#4855C2semidirect
10. C3×#4842C2semidirect
11. C3×#4828C2semidirect
13. C3×#4763C2semidirect
14. C3×#4761C2semidirect
17. #81158C3direct (N × H)
63. #5690C2×C3semidirect
64. D4×Dic6C2×C3semidirect
70. C3×#478D3semidirect
71. C3×#478C2×C3semidirect
80. #5064C2×C3semidirect
82. #4890C2×C3semidirect
83. #4876C2×C3semidirect
84. #4870C2×C3semidirect
85. #4855C2×C3semidirect
86. #4842C2×C3semidirect
87. #4828C2×C3semidirect
89. #4763C2×C3semidirect
90. #4761C2×C3semidirect
117. C3×#213Q8semidirect
252. C3×D12C2×Q8semidirect
264. C3×C3⋊C8C2×Q8semidirect
271. #478C3×D3semidirect
361. #213C3×Q8semidirect
506. D12C2×C3×Q8semidirect
524. C3⋊C8C2×C3×Q8semidirect
628. C32#3384semidirect
699. C3#81158direct (N × H)
700. C3C3×#3384semidirect

Maximal subgroups

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

subgroupindex
C3×#56902
C3×D4×Dic62
C32×#4782
C3×#50642
C3×#50142
C3×#48902
C3×#48762
C3×#48702
C3×#48552
C3×#48422
C3×#48282
C3×#47852
C3×#47632
C3×#47612
C3×#47562
C3×#33843
#811583