Finite Group Databasebeta

← C3×#79440 #11887205

Subgroups — C3×#79440 #11887205

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5550C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3C32×C8×D4C211yesmaximal, characteristic, complemented
4C3×#5116C211yesmaximal, characteristic, complemented
5C3×#5114C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7C2×C3×#821C211yesmaximal, characteristic, complemented
8C3×#4847C211yesmaximal, characteristic, complemented
9C3×#4845C211yesmaximal, characteristic, complemented
10C3×#4737C211yesmaximal, characteristic, complemented
11C3×#4733C211yesmaximal, characteristic, complemented
12C3×#4731C211yesmaximal, characteristic, complemented
13C3×#4721C211yesmaximal, characteristic, complemented
14C3×#4697C211yesmaximal, characteristic, complemented
15C3×C4×#204C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#79440C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×#937—21no—
24C3×#935—21no—
25C3×#930C2211yescharacteristic
26C3×#926C2211yescharacteristic, complemented
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C2×C3×Dic12C2211yescharacteristic, complemented
32C2×C3×#204C2211yescharacteristic
33C2×C3×#204C2211yescharacteristic
34C3×#894—21no—
35C3×#889—21no—
36C3×#884—21no—
37C3×D3×C22⋊C4—21no—
38C3×#879—21no—
39C3×#877—21no—
40C3×#875C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×#870C2211yescharacteristic, complemented
43C3×C4×Dic6C2211yescharacteristic, complemented
44C32×C4⋊C8C2211yescharacteristic, complemented
45C32×C22⋊C8C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic, complemented
47C32×C4×C8C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×#818C2211yescharacteristic, complemented
55C3×#817C2211yescharacteristic, complemented
56C3×#817C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5550C2×C311yescharacteristic
64#5541C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#483—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#467—31no—
70C3×#465—31no—
71C3×#464—31no—
72C3×#452—31no—
73C3×#450—31no—
74C3×C4×SD16—31no—
75C3×C8×D4—21no—
76C3×C8×D4D311yescharacteristic, complemented
77C3×C8×D4C2×C311yescharacteristic, complemented
78C3×#416—31no—
79C2×C3×#102—31no—
80#5116C2×C311yescharacteristic, complemented
81#5114C2×C311yescharacteristic, complemented
82#5113C2×C311yescharacteristic, complemented
83C2×#821C2×C311yescharacteristic, complemented
84#4847C2×C311yescharacteristic, complemented
85#4845C2×C311yescharacteristic, complemented
86#4737C2×C311yescharacteristic, complemented
87#4733C2×C311yescharacteristic, complemented
88#4731C2×C311yescharacteristic, complemented
89#4721C2×C311yescharacteristic, complemented
90#4697C2×C311yescharacteristic, complemented
91C4×#204C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8—41no—
111C2×C32×C8—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4D411yescharacteristic
117C32×C22⋊C4D411yescharacteristic
118C32×C22⋊C4D411yescharacteristic
119C32×C42C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3—21no—
141C3×Dic12—41no—
142C3×#204—22no—
143C3×#204—41no—
144#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#235C22×C311yescharacteristic
148C22×D12C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—21no—
153C22×C3×C8—21no—
154C22×C3×C8C2×D311yescharacteristic
155C22×C3×C8C2×D311yescharacteristic, complemented
156C22×C3×C8C22×C311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic, complemented
158C3×#126—61no—
159C3×#125—31no—
160C3×#125—61no—
161C3×#124—31no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#120—61no—
170C3×C4×Q8—31no—
171C3×C4×D4—21no—
172C3×C4×D4—31no—
173C3×C4×D4C2×D311yescharacteristic
174C3×C4×D4C22×C311yescharacteristic
175C3×#117—31no—
176C3×#117—61no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—61no—
179#937—21no—
180#935—21no—
181#930C22×C311yescharacteristic
182#926C22×C311yescharacteristic, complemented
183C2×C4⋊Dic3C22×C311yescharacteristic
184#924C22×C311yescharacteristic
185#924C22×C311yescharacteristic
186#924C22×C311yescharacteristic, complemented
187C2×Dic12C22×C311yescharacteristic, complemented
188C2×#204C22×C311yescharacteristic
189C2×#204C22×C311yescharacteristic
190#894—21no—
191#889—21no—
192#884—21no—
193D3×C22⋊C4—21no—
194#879—21no—
195#877—21no—
196#875C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198#870C22×C311yescharacteristic, complemented
199C4×Dic6C22×C311yescharacteristic, complemented
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C22×C311yescharacteristic, complemented
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—21no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C2×D311yescharacteristic, complemented
220C3×C22⋊C8C22×C311yescharacteristic
221C3×C22⋊C8C22×C311yescharacteristic, complemented
222C3×C4×C8—21no—
223C3×C4×C8C2×D311yescharacteristic, complemented
224C3×C4×C8C22×C311yescharacteristic, complemented
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229#821C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231#818C22×C311yescharacteristic, complemented
232#817C22×C311yescharacteristic, complemented
233#817C22×C311yescharacteristic, complemented
234#816C22×C311yescharacteristic, complemented
235#816C22×C311yescharacteristic, complemented
236#816C22×C311yescharacteristic, complemented
237#816C22×C311yescharacteristic, complemented
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C32×D4—22no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yes—
269C3×C4×D3—42no—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C32×C8—21no—
278C32×C8—21no—
279#552—31no—
280#546—31no—
281#488—31no—
282#483—31no—
283#482—31no—
284#478—31no—
285#467—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4C3×D311yescharacteristic, complemented
292#416—31no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C2×C3×D4D1211yescharacteristic
309C2×C3×D4C3×D411yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C2×#67—21no—
320C2×#67—21no—
321C22×Dic3—21no—
322#235—22no—
323#235—41no—
324C2×D12—22no—
325C2×D12—21no—
326C2×D12—41no—
327C2×D12C23×C311yescharacteristic
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×Dic6C23×C311yescharacteristic
332C2×Dic6C23×C311yescharacteristic
333C3×Q16—121no—
334C3×SD16—62no—
335C3×SD16—121no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—41no—
341C2×C3×C8—41no—
342C2×C3×C8—41no—
343C2×C3×C8—41no—
344C2×C3×C8—42no—
345C2×C3×C8—42no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C23×C311yescharacteristic
351C2×C3×C8C23×C311yescharacteristic
352C2×C3×C8C23×C311yescharacteristic
353C2×C3×C8C23×C311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4D1211yescharacteristic
367C3×C4⋊C4C3×D411yescharacteristic
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4D1211yescharacteristic
379C3×C22⋊C4D1211yescharacteristic
380C3×C22⋊C4C3×D411yescharacteristic
381C3×C22⋊C4C3×D411yescharacteristic
382C3×C42—21no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C23×C311yescharacteristic
387#217—21no—
388#217—21no—
389#217—21no—
390#217—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3C23×C311yescharacteristic
397C4⋊Dic3C23×C311yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399C4⋊Dic3C23×C311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406C4×Dic3—21no—
407C4×Dic3—21no—
408Dic12—41no—
409#204—22no—
410#204—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32#13512yes—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16—31no—
440C2×SD16—31no—
441C2×SD16—31no—
442C22×C8C2×C3×D311yescharacteristic
443C22×C8C2×C3×D311yescharacteristic, complemented
444#126—61no—
445#125—31no—
446#125—61no—
447#124—31no—
448#123—61no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453#121—31no—
454#121—61no—
455#120—61no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4C2×C3×D311yescharacteristic
459#117—31no—
460#117—61no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—61no—
463#107—31no—
464#106—31no—
465#106—31no—
466C4⋊C8C2×C3×D311yescharacteristic, complemented
467#103—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477C22⋊C8C2×C3×D311yescharacteristic
478C22⋊C8C2×C3×D311yescharacteristic, complemented
479C4×C8C2×C3×D311yescharacteristic, complemented
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3C2×D1211yescharacteristic
488C23×C3C2×D1211yescharacteristic
489C23×C3C2×C3×D411yescharacteristic
490C23×C3C2×C3×D411yescharacteristic
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—81no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—24no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—32no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—122no—
508C3×D4—122no—
509C3×D4—241no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4—241no—
536C2×C3×C4C2×D1211yescharacteristic
537C2×C3×C4C2×D1211yescharacteristic
538C2×C3×C4C2×D1211yescharacteristic
539C2×C3×C4C2×D1211yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C2×C3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C2×C3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C24×C311yescharacteristic
546#67—42no—
547#67—81no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—42no—
555D12—21no—
556D12—21no—
557D12—21no—
558D12—42no—
559D12C3×#4112yes—
560C4×D3—42no—
561C4×D3—81no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566C3×C8—22no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—41no—
577C3×C8—41no—
578C2×C32—22no—
579C2×C32—41no—
580C2×C32#54611yescharacteristic
581C2×C32C2×#13511yescharacteristic
582C2×C32#57711yescharacteristic
583C3×D3—42no—
584C3×D3—81no—
585C24—61no—
586#41—62no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—121no—
597C2×D4C3×D1211yescharacteristic
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4C22×C3×D311yescharacteristic
602C22×C4C22×C3×D311yescharacteristic
603Q16—121no—
604SD16—62no—
605SD16—121no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8C22×C3×D311yescharacteristic
609C2×C8C22×C3×D311yescharacteristic
610C2×C8C22×C3×D311yescharacteristic
611C2×C8C22×C3×D311yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4C3×D1211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4C3×D1211yescharacteristic
633C22⋊C4C3×D1211yescharacteristic
634C42—61no—
635C42—61no—
636C42C22×C3×D311yescharacteristic
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—21no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—62no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—244no—
661C22×C3#90412yes—
662C22×C3C3×#13512yes—
663C22×C3C22×D1211yescharacteristic
664C22×C3C22×C3×D411yescharacteristic
665C2×D3—22no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—84no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4#100411yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4C2×C3×#4111yescharacteristic
695C3×C4C3×H(5,𝔽2)11yescharacteristic
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—61no—
704C23—61no—
705C23—122no—
706C23—122no—
707C23—241no—
708C23C2×C3×D1211yescharacteristic
709C23C2×C3×D1211yescharacteristic
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—61no—
714D4—22no—
715D4—32no—
716D4—61no—
717D4—61no—
718D4—61no—
719D4—122no—
720D4—122no—
721D4—241no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—241no—
735C2×C4C2×C3×D1211yescharacteristic
736C2×C4C2×C3×D1211yescharacteristic
737C2×C4C2×C3×D1211yescharacteristic
738C2×C4C2×C3×D1211yescharacteristic
739C2×C4C23×C3×D311yescharacteristic
740C8—21no—
741C8—21no—
742C8—21no—
743C8—21no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—42no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—122no—
754C2×C3—241no—
755C2×C3#555411yescharacteristic
756C2×C3C2×#90411yescharacteristic
757C2×C3#575111yescharacteristic
758C2×C3C3×#54611yescharacteristic
759C2×C3C2×C3×#13511yescharacteristic
760C2×C3C3×#57711yescharacteristic
761D3—42no—
762D3—81no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—244no—
775C22C3×#90412yes—
776C22C22×C3×D1211yescharacteristic
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4C3×#100411yescharacteristic
788C4C3×D3×#4111yescharacteristic
789C3—21no—
790C3#7944011yescharacteristic, direct product factor
791C3C3×#329611yescharacteristic, complemented
792C2—22no—
793C2—41no—
794C2—122no—
795C2—241no—
796C2C3×#555411yescharacteristic
797C2C2×C3×#90411yescharacteristic
798C2C3×#575111yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C8×D4C2
socleC22×C32C22×D4
prime radicalC3×#5550C2
hypercenterC3×C8×D4D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5541C2semidirect
3. C32×C8×D4C2semidirect
4. C3×#5116C2semidirect
5. C3×#5114C2semidirect
6. C3×#5113C2semidirect
7. C2×C3×#821C2semidirect
8. C3×#4847C2semidirect
9. C3×#4845C2semidirect
10. C3×#4737C2semidirect
11. C3×#4733C2semidirect
12. C3×#4731C2semidirect
13. C3×#4721C2semidirect
14. C3×#4697C2semidirect
15. C3×C4×#204C2semidirect
17. #79440C3direct (N × H)
21. C22×C32×C8C22semidirect
26. C3×#926C22semidirect
30. C3×#924C22semidirect
31. C2×C3×Dic12C22semidirect
42. C3×#870C22semidirect
43. C3×C4×Dic6C22semidirect
44. C32×C4⋊C8C22semidirect
46. C32×C22⋊C8C22semidirect
47. C32×C4×C8C22semidirect
54. C3×#818C22semidirect
55. C3×#817C22semidirect
56. C3×#817C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. C3×#816C22semidirect
60. C3×#816C22semidirect
64. #5541C2×C3semidirect
76. C3×C8×D4D3semidirect
77. C3×C8×D4C2×C3semidirect
80. #5116C2×C3semidirect
81. #5114C2×C3semidirect
82. #5113C2×C3semidirect
83. C2×#821C2×C3semidirect
84. #4847C2×C3semidirect
85. #4845C2×C3semidirect
86. #4737C2×C3semidirect
87. #4733C2×C3semidirect
88. #4731C2×C3semidirect
89. #4721C2×C3semidirect
90. #4697C2×C3semidirect
91. C4×#204C2×C3semidirect
155. C22×C3×C8C2×D3semidirect
157. C22×C3×C8C22×C3semidirect
182. #926C22×C3semidirect
186. #924C22×C3semidirect
187. C2×Dic12C22×C3semidirect
198. #870C22×C3semidirect
199. C4×Dic6C22×C3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C22×C3semidirect
219. C3×C22⋊C8C2×D3semidirect
221. C3×C22⋊C8C22×C3semidirect
223. C3×C4×C8C2×D3semidirect
224. C3×C4×C8C22×C3semidirect
231. #818C22×C3semidirect
232. #817C22×C3semidirect
233. #817C22×C3semidirect
234. #816C22×C3semidirect
235. #816C22×C3semidirect
236. #816C22×C3semidirect
237. #816C22×C3semidirect
291. C8×D4C3×D3semidirect
443. C22×C8C2×C3×D3semidirect
466. C4⋊C8C2×C3×D3semidirect
478. C22⋊C8C2×C3×D3semidirect
479. C4×C8C2×C3×D3semidirect
702. C32#3296semidirect
790. C3#79440direct (N × H)
791. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#55502
C3×#55412
C32×C8×D42
C3×#51162
C3×#51142
C3×#51132
C2×C3×#8212
C3×#48472
C3×#48452
C3×#47372
C3×#47332
C3×#47312
C3×#47212
C3×#46972
C3×C4×#2042
C3×#32963
#794403