Finite Group Databasebeta

← C3×#79624 #11895625

Subgroups — C3×#79624 #11895625

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5569C211yesmaximal, characteristic, complemented
2C3×#5559C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5166C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic
6C3×#5028C211yesmaximal, characteristic, complemented
7C3×#5009C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4854C211yesmaximal, characteristic, complemented
10C3×#4790C211yesmaximal, characteristic, complemented
11C3×#4788C211yesmaximal, characteristic, complemented
12C3×#4768C211yesmaximal, characteristic, complemented
13C3×#4760C211yesmaximal, characteristic
14C3×#4697C211yesmaximal, characteristic, complemented
15C3×C8×Dic6C211yesmaximal, characteristic, complemented
16C3×#3365—31nomaximal
17#79624C311yesmaximal, characteristic, direct product factor
18C2×C32×SD16C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#940C2211yescharacteristic
26C3×#936C2211yescharacteristic
27C3×#929—21no—
28C3×C4×#67—21no—
29C3×#893C2211yescharacteristic
30C3×#890—21no—
31C3×#890C2211yescharacteristic
32C3×#888—21no—
33C3×#888C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#885—21no—
36C3×#883—21no—
37C3×#875C2211yescharacteristic
38C3×#870—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6—21no—
41C3×C4×Dic6C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C4×C8C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#559—31no—
62C3×#557—31no—
63#5569C2×C311yescharacteristic, complemented
64#5559C2×C311yescharacteristic
65C3×#488—31no—
66C3×#488—31no—
67C3×#486—31no—
68C3×#478—31no—
69C3×#478—31no—
70C3×#475—31no—
71C3×#464—31no—
72C3×#464—31no—
73C3×#460—31no—
74C3×C8×Q8—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—21no—
77C3×C4×SD16—31no—
78C3×C4×SD16D311yescharacteristic, complemented
79C3×C4×SD16C2×C311yescharacteristic, complemented
80#5166C2×C311yescharacteristic, complemented
81#5163C2×C311yescharacteristic
82#5028C2×C311yescharacteristic, complemented
83#5009C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4854C2×C311yescharacteristic, complemented
86#4790C2×C311yescharacteristic, complemented
87#4788C2×C311yescharacteristic, complemented
88#4768C2×C311yescharacteristic, complemented
89#4760C2×C311yescharacteristic
90#4697C2×C311yescharacteristic, complemented
91C8×Dic6C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6D411yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C32×SD16—22no—
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×#216—22no—
114C3×#215—22no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3365—31noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—21no—
141C2×C3×SD16—31no—
142C2×C3×SD16C2×D311yescharacteristic
143C2×C3×SD16C22×C311yescharacteristic
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—61no—
146C3×#127—31no—
147C3×#125—31no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×#124—31no—
152C3×#124—31no—
153C3×#124—61no—
154C3×#123—61no—
155C3×#123—61no—
156C3×C4×Q8—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—61no—
162C3×C4×Q8C2×D311yescharacteristic
163C3×C4×Q8C22×C311yescharacteristic
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4C2×D311yescharacteristic
168C3×C4×D4C22×C311yescharacteristic
169Q8×Dic3C22×C311yescharacteristic
170Q8×Dic3C22×C311yescharacteristic
171C2×#216C22×C311yescharacteristic
172C2×#215C22×C311yescharacteristic
173#940C22×C311yescharacteristic
174#936C22×C311yescharacteristic
175#929—21no—
176C4×#67—21no—
177#893C22×C311yescharacteristic
178#890—21no—
179#890C22×C311yescharacteristic
180#888—21no—
181#888C22×C311yescharacteristic
182#887C22×C311yescharacteristic
183#885—21no—
184#883—21no—
185#875C22×C311yescharacteristic
186#870—21no—
187#870C22×C311yescharacteristic
188C4×Dic6—21no—
189C4×Dic6C22×C311yescharacteristic
190C3×#107—31no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106C2×D311yescharacteristic
194C3×#106C22×C311yescharacteristic
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#103—21no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C22×C311yescharacteristic
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×C4×C8—21no—
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215C3×C4×C8C2×D311yescharacteristic
216C3×C4×C8C22×C311yescharacteristic
217#832C22×C311yescharacteristic
218#832C22×C311yescharacteristic
219#821C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#816C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8#4112yes—
236C32×D4—21no—
237C32×D4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—81no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C3×#67—42no—
246C3×#67—81no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×C4×D3—81no—
257C3×Dic6—22no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—42no—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—31no—
266#557—31no—
267#488—31no—
268#488—31no—
269#486—31no—
270#478—31no—
271#478—31no—
272#475—31no—
273#464—31no—
274#464—31no—
275#460—31no—
276C8×Q8—31no—
277C4×Q16—31no—
278C4×SD16—31no—
279C4×SD16C3×D311yescharacteristic, complemented
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C23×C311yescharacteristic
286C2×C3×D4—21no—
287C2×C3×D4—31no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4C22×D311yescharacteristic
291C2×C3×D4C23×C311yescharacteristic
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—41no—
295C22×C3×C4—61no—
296C2×#67—21no—
297C2×#67—21no—
298C2×D12C23×C311yescharacteristic
299C2×C4×D3—21no—
300C2×Dic6—21no—
301C2×Dic6C3×D411yescharacteristic
302C2×Dic6C23×C311yescharacteristic
303C3×Q16—62no—
304C3×SD16—24no—
305C3×SD16—22no—
306C3×SD16—22no—
307C3×SD16—62no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C23×C311yescharacteristic
315C2×C3×C8C23×C311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—41no—
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⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—41no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—41no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C23×C311yescharacteristic
357#217—21no—
358#217—21no—
359#216—22no—
360#215—22no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364C4⋊Dic3—21no—
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3C3×D411yescharacteristic
368C4⋊Dic3C23×C311yescharacteristic
369C4⋊Dic3C23×C311yescharacteristic
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4C3×D411yescharacteristic
376Dic3⋊C4C3×D411yescharacteristic
377C4×Dic3—21no—
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3C23×C311yescharacteristic
381C4×Dic3C23×C311yescharacteristic
382C2×C3⋊C8C23×C311yescharacteristic
383C2×C3⋊C8C23×C311yescharacteristic
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32C22×D411yescharacteristic
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—21no—
392C32×C4—22no—
393C32×C4—21no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4C2×#4111yescharacteristic
397C32×C42−1+411yescharacteristic
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#13512yes—
405C2×Q16—31no—
406C2×SD16—31no—
407C2×SD16C2×C3×D311yescharacteristic
408C4⋊Q8—31no—
409C4⋊Q8—61no—
410#127—31no—
411#125—31no—
412#125—31no—
413#125—61no—
414#125—61no—
415#124—31no—
416#124—31no—
417#124—61no—
418#123—61no—
419#123—61no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—61no—
425C4×Q8C2×C3×D311yescharacteristic
426C4×D4—31no—
427C4×D4—61no—
428C4×D4C2×C3×D311yescharacteristic
429#107—31no—
430#106—31no—
431#106C2×C3×D311yescharacteristic
432C4⋊C8—31no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435#103—31no—
436#103—31no—
437#103—31no—
438#103C2×C3×D311yescharacteristic
439#102—31no—
440#102—31no—
441#102—31no—
442#102—31no—
443#102—31no—
444#102C2×C3×D311yescharacteristic
445C4×C8—31no—
446C4×C8—31no—
447C4×C8C2×C3×D311yescharacteristic
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—41no—
451C23×C3—61no—
452C22×D3—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—62no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—122no—
461C3×Q8#23512yes—
462C3×Q8C3×#4112yes—
463C3×D4—22no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—41no—
469C3×D4—61no—
470C3×D4—61no—
471C3×D4—122no—
472C3×D4—241no—
473C2×C3×C4—21no—
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—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—81no—
493C2×C3×C4—81no—
494C2×C3×C4—82no—
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
502#67—42no—
503#67—81no—
504C2×Dic3—21no—
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—
513C4×D3—81no—
514Dic6—22no—
515Dic6—21no—
516Dic6—21no—
517Dic6—42no—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C2×C32—81no—
529C2×C32#54811yescharacteristic
530C2×C32C2×#13511yescharacteristic
531C2×C32#57711yescharacteristic
532C3×D3—81no—
533C2×Q8—31no—
534C2×Q8—31no—
535C2×Q8—61no—
536C2×Q8C22×C3×D311yescharacteristic
537C2×D4—31no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4C22×C3×D311yescharacteristic
541C22×C4—21no—
542C22×C4—61no—
543Q16—62no—
544SD16—22no—
545SD16—62no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8C22×C3×D311yescharacteristic
549C2×C8C22×C3×D311yescharacteristic
550C4⋊C4—21no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
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—21no—
573C42—31no—
574C42—31no—
575C42—61no—
576C42—61no—
577C42—61no—
578C42C22×C3×D311yescharacteristic
579C22×C3—21no—
580C22×C3—42no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3C2×D3×D411yescharacteristic
593C22×C3C22×C3×D411yescharacteristic
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C3×C4—22no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—32no—
607C3×C4—41no—
608C3×C4—42no—
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×C4C2×#23511yescharacteristic
622C3×C4#101011yescharacteristic
623C3×C4C2×C3×#4111yescharacteristic
624C3×C4C3×2−1+411yescharacteristic
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—41no—
629Dic3—41no—
630Dic3—41no—
631Dic3C3×#13512yes—
632C32#336511yescharacteristic, complemented, Sylow
633C23—21no—
634C23—61no—
635Q8—21no—
636Q8—62no—
637Q8—61no—
638Q8—61no—
639Q8—122no—
640Q8C3×#23512yes—
641D4—21no—
642D4—21no—
643D4—61no—
644D4—61no—
645D4—122no—
646D4—241no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—81no—
658C2×C4—241no—
659C2×C4C3×D3×D411yescharacteristic
660C2×C4C3×D3×D411yescharacteristic
661C2×C4C23×C3×D311yescharacteristic
662C8—21no—
663C8—21no—
664C8—61no—
665C8—61no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—82no—
670C2×C3—81no—
671C2×C3—81no—
672C2×C3—241no—
673C2×C3#555211yescharacteristic
674C2×C3#576211yescharacteristic
675C2×C3D3×#13511yescharacteristic
676C2×C3C3×#54811yescharacteristic
677C2×C3C2×C3×#13511yescharacteristic
678C2×C3C3×#57711yescharacteristic
679D3—81no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—121no—
684C22—121no—
685C22—121no—
686C22C2×C3×D3×D411yescharacteristic
687C4—21no—
688C4—21no—
689C4—22no—
690C4—32no—
691C4—41no—
692C4—41no—
693C4—61no—
694C4—61no—
695C4—61no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4C2×C3×#23511yescharacteristic
700C4C3×#101011yescharacteristic
701C3—21no—
702C3#7962411yescharacteristic, direct product factor
703C3C3×#336511yescharacteristic, complemented
704C2—81no—
705C2—241no—
706C2C3×#555211yescharacteristic
707C2C3×#576211yescharacteristic
708C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#5569C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5166C2semidirect
6. C3×#5028C2semidirect
7. C3×#5009C2semidirect
8. C3×#4871C2semidirect
9. C3×#4854C2semidirect
10. C3×#4790C2semidirect
11. C3×#4788C2semidirect
12. C3×#4768C2semidirect
14. C3×#4697C2semidirect
15. C3×C8×Dic6C2semidirect
17. #79624C3direct (N × H)
63. #5569C2×C3semidirect
78. C3×C4×SD16D3semidirect
79. C3×C4×SD16C2×C3semidirect
80. #5166C2×C3semidirect
82. #5028C2×C3semidirect
83. #5009C2×C3semidirect
84. #4871C2×C3semidirect
85. #4854C2×C3semidirect
86. #4790C2×C3semidirect
87. #4788C2×C3semidirect
88. #4768C2×C3semidirect
90. #4697C2×C3semidirect
91. C8×Dic6C2×C3semidirect
279. C4×SD16C3×D3semidirect
632. C32#3365semidirect
702. C3#79624direct (N × H)
703. C3C3×#3365semidirect

Maximal subgroups

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

subgroupindex
C3×#55692
C3×#55592
C32×C4×SD162
C3×#51662
C3×#51632
C3×#50282
C3×#50092
C3×#48712
C3×#48542
C3×#47902
C3×#47882
C3×#47682
C3×#47602
C3×#46972
C3×C8×Dic62
C3×#33653
#796243