Finite Group Databasebeta

← C3×#84001 #11868006

Subgroups — C3×#84001 #11868006

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#575C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3C2×C3×#950C211yesmaximal, characteristic, complemented
4C2×C3×#948C211yesmaximal, characteristic, complemented
5C3×#5237C211yesmaximal, characteristic, complemented
6C3×#5204C212yesmaximal, complemented
7C3×#5203C212yesmaximal, complemented
8C3×#5200C212yesmaximal, complemented
9C3×#5199C212yesmaximal, complemented
10C3×#5132C211yesmaximal, characteristic, complemented
11C2×C3×#822C211yesmaximal, characteristic, complemented
12C3×#3067—31nomaximal
13#84001C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C32×#41C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C32×#137—21no—
18C32×#137C2212yes—
19C32×AGL(1,ℤ/8)—21no—
20C32×AGL(1,ℤ/8)C2212yes—
21C32×#135—22no—
22C2×C32×M16C2211yescharacteristic
23C3×#951C2212yes—
24C3×#950—22no—
25C3×#950—21no—
26C3×#950—21no—
27C3×#950—21no—
28C3×#950—21no—
29C3×#949C2212yes—
30C3×#948—21no—
31C3×#948—21no—
32C3×#948C2212yes—
33C3×#948C2212yes—
34C2×C3×#216C2211yescharacteristic, complemented
35C3×#942—21no—
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#214C2211yescharacteristic, complemented
38C3×#932—21no—
39C2×C3×#213C2211yescharacteristic, complemented
40C2×C3×#208—21no—
41C2×C3×#208C2211yescharacteristic
42C2×C3×#208C2211yescharacteristic
43C22×C3×C3⋊C8—21no—
44C22×C3×C3⋊C8C2211yescharacteristic
45C3×#836C2212yescomplemented
46C3×#833C2212yescomplemented
47C3×#824C2212yescomplemented
48C3×#823C2212yescomplemented
49C3×#822C2212yescomplemented
50C3×#822C2212yescomplemented
51C3×#575—21no—
52C3×#575—31no—
53C3×#575D311yescharacteristic, complemented
54C3×#575C2×C311yescharacteristic, complemented
55C2×C3×#135—31no—
56C2×C3×#131—31no—
57#5822C2×C311yescharacteristic, complemented
58C2×#950C2×C311yescharacteristic, complemented
59C2×#948C2×C311yescharacteristic, complemented
60C3×#473—32no—
61C3×#472—32no—
62C3×#471—32no—
63C3×#471—32no—
64C2×C3×#108—31no—
65C3×#413—31no—
66C3×#413—31no—
67#5237C2×C311yescharacteristic, complemented
68#5204C2×C312yescomplemented
69#5203C2×C312yescomplemented
70#5200C2×C312yescomplemented
71#5199C2×C312yescomplemented
72#5132C2×C311yescharacteristic, complemented
73C2×#822C2×C311yescharacteristic, complemented
74C32×#41—21no—
75C32×#41—21no—
76C32×#41—21no—
77C32×#41—21no—
78C32×#41—21no—
79C32×#41—21no—
80C32×#41D412yes—
81C32×#41C2312yes—
82C2×C32×Q8D411yescharacteristic
83C2×C32×Q8C2311yescharacteristic
84C2×C32×D4—21no—
85C2×C32×D4—21no—
86C2×C32×D4D411yescharacteristic
87C2×C32×D4C2311yescharacteristic
88C22×C32×C4—21no—
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C2×C3×#67—21no—
92C3×#235—21no—
93C3×#235—21no—
94C3×#235—21no—
95C3×#235—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×Dic6C2311yescharacteristic
99C32×Q16—22no—
100C32×SD16—22no—
101C32×SD16—22no—
102C32×D8—22no—
103C32×M16—21no—
104C32×M16C2312yes—
105C2×C32×C8—21no—
106C3×#216—22no—
107C3×#216—21no—
108C3×#216—21no—
109C3×#215—22no—
110C3×#215—21no—
111C3×#215—21no—
112C3×#214—22no—
113C3×#214—21no—
114C3×#214—21no—
115C3×#213—22no—
116C3×#213—21no—
117C3×#213—21no—
118C3×#208—21no—
119C3×#208—21no—
120C3×#208—22no—
121C3×#208—22no—
122C3×#208C2312yes—
123C3×#208C2312yes—
124C2×C3×C3⋊C8—21no—
125C2×C3×C3⋊C8—21no—
126C2×C3×C3⋊C8—22no—
127C2×C3×C3⋊C8—22no—
128C2×C3×C3⋊C8D411yescharacteristic
129C2×C3×C3⋊C8D411yescharacteristic
130C2×C3×C3⋊C8D411yescharacteristic
131C2×C3×C3⋊C8D411yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3067—31noSylow
135C2×C3×#41—21no—
136C2×C3×#41—21no—
137C2×C3×#41—31no—
138C2×C3×#41C2×D311yescharacteristic
139C2×C3×#41C2×D311yescharacteristic
140C2×C3×#41C22×C311yescharacteristic
141C2×C3×#41C22×C311yescharacteristic
142C2×#235C22×C311yescharacteristic
143C3×#137—22no—
144C3×#137—21no—
145C3×#137—21no—
146C3×#137—22no—
147C3×#137—32no—
148C3×#137—61no—
149C3×#137C2×D312yes—
150C3×#137C22×C312yes—
151C3×AGL(1,ℤ/8)—22no—
152C3×AGL(1,ℤ/8)—21no—
153C3×AGL(1,ℤ/8)—21no—
154C3×AGL(1,ℤ/8)—22no—
155C3×AGL(1,ℤ/8)—32no—
156C3×AGL(1,ℤ/8)—61no—
157C3×AGL(1,ℤ/8)C2×D312yes—
158C3×AGL(1,ℤ/8)C22×C312yes—
159C3×#135—24no—
160C3×#135—22no—
161C3×#135—22no—
162C3×#135—61no—
163C3×#135—61no—
164C3×#135—61no—
165C3×#135—61no—
166C3×#135—62no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C3×#131—32no—
172C3×#131—32no—
173C3×#131—61no—
174C3×#131—61no—
175C2×C3×M16—21no—
176C2×C3×M16—31no—
177C2×C3×M16—31no—
178C2×C3×M16—61no—
179C2×C3×M16C2×D311yescharacteristic
180C2×C3×M16C22×C311yescharacteristic
181C22×C3×C8—31no—
182C22×C3×C8—61no—
183#951C22×C312yes—
184#950—22no—
185#950—21no—
186#950—21no—
187#950—21no—
188#950—21no—
189#949C22×C312yes—
190#948—21no—
191#948—21no—
192#948C22×C312yes—
193#948C22×C312yes—
194C2×#216C22×C311yescharacteristic, complemented
195#942—21no—
196C2×#215C22×C311yescharacteristic, complemented
197C2×#214C22×C311yescharacteristic, complemented
198#932—21no—
199C2×#213C22×C311yescharacteristic, complemented
200C2×#208—21no—
201C2×#208C22×C311yescharacteristic
202C2×#208C22×C311yescharacteristic
203C22×C3⋊C8—21no—
204C22×C3⋊C8C22×C311yescharacteristic
205C3×#108—32no—
206C3×#108—32no—
207C3×#101—32no—
208C3×#101—32no—
209C3×#100—32no—
210C3×#100—32no—
211#836C22×C312yescomplemented
212#833C22×C312yescomplemented
213#824C22×C312yescomplemented
214#823C22×C312yescomplemented
215#822C22×C312yescomplemented
216#822C22×C312yescomplemented
217C23×C32—21no—
218C23×C32—21no—
219C23×C32#4111yescharacteristic
220C22×C3×D3—21no—
221C32×Q8—21no—
222C32×Q8—21no—
223C32×Q8—21no—
224C32×Q8C2×D412yes—
225C32×D4—21no—
226C32×D4—22no—
227C32×D4—22no—
228C32×D4—21no—
229C32×D4—21no—
230C32×D4—41no—
231C32×D4—41no—
232C32×D4C2×D412yes—
233C2×C32×C4—21no—
234C2×C32×C4—22no—
235C2×C32×C4—22no—
236C2×C32×C4—21no—
237C2×C32×C4—41no—
238C2×C32×C4—41no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4#4111yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C3×#67—41no—
246C3×#67—41no—
247C2×C3×Dic3—21no—
248C3×D12—21no—
249C3×D12—21no—
250C3×C4×D3—41no—
251C3×C4×D3—41no—
252C3×Dic6—21no—
253C3×Dic6—21no—
254C32×C8—22no—
255C3×C3⋊C8—22no—
256C3×C3⋊C8—22no—
257C3×C3⋊C8C2×D411yescharacteristic
258C3×C3⋊C8C2×D411yescharacteristic
259C3×C3⋊C8C2×D411yescharacteristic
260C3×C3⋊C8C2×D411yescharacteristic
261#575—31no—
262#575C3×D311yescharacteristic, complemented
263C2×#135—31no—
264C2×#131—31no—
265#473—32no—
266#472—32no—
267#471—32no—
268#471—32no—
269C2×#108—31no—
270#413—31no—
271#413—31no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—21no—
276C3×#41—22no—
277C3×#41—22no—
278C3×#41—21no—
279C3×#41—21no—
280C3×#41—21no—
281C3×#41—21no—
282C3×#41—21no—
283C3×#41—21no—
284C3×#41—21no—
285C3×#41—21no—
286C3×#41—22no—
287C3×#41—22no—
288C3×#41—41no—
289C3×#41—41no—
290C3×#41—41no—
291C3×#41—41no—
292C3×#41—61no—
293C3×#41—61no—
294C3×#41—61no—
295C3×#41—61no—
296C3×#41#6712yes—
297C3×#41C3×D412yes—
298C3×#41C22×D312yes—
299C3×#41C23×C312yes—
300C2×C3×Q8—21no—
301C2×C3×Q8—21no—
302C2×C3×Q8—31no—
303C2×C3×Q8#6711yescharacteristic
304C2×C3×Q8C3×D411yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C23×C311yescharacteristic
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—31no—
314C2×C3×D4—41no—
315C2×C3×D4—41no—
316C2×C3×D4—61no—
317C2×C3×D4#6711yescharacteristic
318C2×C3×D4C3×D411yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C23×C311yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—41no—
327C22×C3×C4—41no—
328C22×C3×C4—61no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C23×C311yescharacteristic
331C2×#67—21no—
332#235—21no—
333#235—21no—
334#235—21no—
335#235—21no—
336C2×D12C23×C311yescharacteristic
337C2×C4×D3—21no—
338C2×Dic6C23×C311yescharacteristic
339C3×Q16—24no—
340C3×Q16—22no—
341C3×Q16—22no—
342C3×Q16—61no—
343C3×Q16—61no—
344C3×Q16—62no—
345C3×SD16—24no—
346C3×SD16—24no—
347C3×SD16—22no—
348C3×SD16—22no—
349C3×SD16—22no—
350C3×SD16—22no—
351C3×SD16—61no—
352C3×SD16—61no—
353C3×SD16—61no—
354C3×SD16—61no—
355C3×SD16—62no—
356C3×SD16—62no—
357C3×D8—24no—
358C3×D8—22no—
359C3×D8—22no—
360C3×D8—61no—
361C3×D8—61no—
362C3×D8—62no—
363C3×M16—22no—
364C3×M16—21no—
365C3×M16—21no—
366C3×M16—22no—
367C3×M16—32no—
368C3×M16—32no—
369C3×M16—62no—
370C3×M16—62no—
371C3×M16—61no—
372C3×M16—61no—
373C3×M16C22×D312yes—
374C3×M16C23×C312yes—
375C2×C3×C8—22no—
376C2×C3×C8—21no—
377C2×C3×C8—21no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—62no—
385C2×C3×C8—62no—
386C2×C3×C8—61no—
387C2×C3×C8—61no—
388#216—22no—
389#216—21no—
390#216—21no—
391#215—22no—
392#215—21no—
393#215—21no—
394#214—22no—
395#214—21no—
396#214—21no—
397#213—22no—
398#213—21no—
399#213—21no—
400#208—21no—
401#208—21no—
402#208—22no—
403#208—22no—
404#208C23×C312yes—
405#208C23×C312yes—
406C2×C3⋊C8—21no—
407C2×C3⋊C8—21no—
408C2×C3⋊C8—22no—
409C2×C3⋊C8—22no—
410C2×C3⋊C8C3×D411yescharacteristic
411C2×C3⋊C8C3×D411yescharacteristic
412C2×C3⋊C8C3×D411yescharacteristic
413C2×C3⋊C8C3×D411yescharacteristic
414C2×C3⋊C8C23×C311yescharacteristic
415C2×C3⋊C8C23×C311yescharacteristic
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—42no—
420C22×C32—81no—
421C22×C32#12111yescharacteristic
422C22×C32#12111yescharacteristic
423C22×C32C2×#4111yescharacteristic
424C2×C3×D3—41no—
425C2×C3×D3—81no—
426C32×C4—22no—
427C32×C4—41no—
428C32×C4#12111yescharacteristic
429C32×C4#12111yescharacteristic
430C32×C4C22×D411yescharacteristic
431C32×C4C22×D411yescharacteristic
432C3×Dic3—41no—
433C2×#41—31no—
434C2×#41C2×C3×D311yescharacteristic
435C2×#41C2×C3×D311yescharacteristic
436#137—21no—
437#137—32no—
438#137—61no—
439#137C2×C3×D312yes—
440AGL(1,ℤ/8)—21no—
441AGL(1,ℤ/8)—32no—
442AGL(1,ℤ/8)—61no—
443AGL(1,ℤ/8)C2×C3×D312yes—
444#135—22no—
445#135—61no—
446#135—61no—
447#135—61no—
448#135—61no—
449#135—62no—
450C2×Q16—31no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×D8—31no—
454#131—32no—
455#131—32no—
456#131—61no—
457#131—61no—
458C2×M16—31no—
459C2×M16—31no—
460C2×M16—61no—
461C2×M16C2×C3×D311yescharacteristic
462C22×C8—31no—
463C22×C8—61no—
464#108—32no—
465#108—32no—
466#101—32no—
467#101—32no—
468#100—32no—
469#100—32no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—61no—
478C23×C3#23711yescharacteristic
479C23×C3C3×#4111yescharacteristic
480C22×D3—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—22no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—22no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8C2×#6712yes—
494C3×Q8C2×C3×D412yes—
495C3×D4—22no—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—42no—
510C3×D4—42no—
511C3×D4—42no—
512C3×D4—42no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—121no—
520C3×D4—121no—
521C3×D4C2×#6712yes—
522C3×D4C2×C3×D412yes—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—42no—
538C2×C3×C4—42no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—42no—
542C2×C3×C4—42no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—121no—
549C2×C3×C4—121no—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4#23711yescharacteristic
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C2×#6711yescharacteristic
555C2×C3×C4C2×C3×D411yescharacteristic
556C2×C3×C4C2×C3×D411yescharacteristic
557C2×C3×C4C2×C3×D411yescharacteristic
558C2×C3×C4C2×C3×D411yescharacteristic
559C2×C3×C4C3×#4111yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C24×C311yescharacteristic
562#67—41no—
563#67—41no—
564C2×Dic3—21no—
565D12—21no—
566D12—21no—
567C4×D3—41no—
568C4×D3—41no—
569Dic6—21no—
570Dic6—21no—
571C3×C8—24no—
572C3×C8—22no—
573C3×C8—22no—
574C3×C8—31no—
575C3×C8—31no—
576C3×C8—31no—
577C3×C8—31no—
578C3×C8—62no—
579C3×C8—62no—
580C3⋊C8—22no—
581C3⋊C8—22no—
582C3⋊C8C2×C3×D411yescharacteristic
583C3⋊C8C2×C3×D411yescharacteristic
584C3⋊C8C2×C3×D411yescharacteristic
585C3⋊C8C2×C3×D411yescharacteristic
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—42no—
590C2×C32—81no—
591C2×C32C2×#12111yescharacteristic
592C3×D3—81no—
593#41—21no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—61no—
600#41—61no—
601#41—61no—
602#41—61no—
603#41C3×#6712yes—
604#41C22×C3×D312yes—
605C2×Q8—31no—
606C2×Q8C3×#6711yescharacteristic
607C2×Q8C22×C3×D311yescharacteristic
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—31no—
611C2×D4—61no—
612C2×D4C3×#6711yescharacteristic
613C2×D4C22×C3×D311yescharacteristic
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—61no—
617C22×C4C22×C3×D311yescharacteristic
618Q16—22no—
619Q16—61no—
620Q16—61no—
621Q16—62no—
622SD16—22no—
623SD16—22no—
624SD16—61no—
625SD16—61no—
626SD16—61no—
627SD16—61no—
628SD16—62no—
629SD16—62no—
630D8—22no—
631D8—61no—
632D8—61no—
633D8—62no—
634M16—21no—
635M16—32no—
636M16—32no—
637M16—62no—
638M16—62no—
639M16—61no—
640M16—61no—
641M16C22×C3×D312yes—
642C2×C8—21no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—31no—
646C2×C8—31no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—62no—
650C2×C8—62no—
651C2×C8—61no—
652C2×C8—61no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—42no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—81no—
667C22×C3—82no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—82no—
671C22×C3—121no—
672C22×C3—241no—
673C22×C3#93911yescharacteristic
674C22×C3#93911yescharacteristic
675C22×C3C3×#12111yescharacteristic
676C22×C3C3×#12111yescharacteristic
677C22×C3C2×#23711yescharacteristic
678C22×C3C2×C3×#4111yescharacteristic
679C2×D3—41no—
680C2×D3—81no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—42no—
688C3×C4—42no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—121no—
692C3×C4#93911yescharacteristic
693C3×C4#93911yescharacteristic
694C3×C4C3×#12111yescharacteristic
695C3×C4C3×#12111yescharacteristic
696C3×C4C2×D3×D411yescharacteristic
697C3×C4C22×#6711yescharacteristic
698C3×C4C22×C3×D411yescharacteristic
699C3×C4C22×C3×D411yescharacteristic
700Dic3—41no—
701C32#306711yescharacteristic, complemented, Sylow
702C23—21no—
703C23—21no—
704C23—61no—
705C23C3×#23711yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—21no—
709Q8—61no—
710Q8—61no—
711Q8C2×C3×#6712yes—
712D4—22no—
713D4—22no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—41no—
718D4—41no—
719D4—61no—
720D4—61no—
721D4—121no—
722D4—121no—
723D4C2×C3×#6712yes—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—61no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4C3×D3×D411yescharacteristic
734C2×C4C3×D3×D411yescharacteristic
735C2×C4C3×#23711yescharacteristic
736C2×C4C2×C3×#6711yescharacteristic
737C2×C4C2×C3×#6711yescharacteristic
738C2×C4C23×C3×D311yescharacteristic
739C8—22no—
740C8—31no—
741C8—31no—
742C8—31no—
743C8—31no—
744C8—62no—
745C8—62no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—41no—
756C2×C3—42no—
757C2×C3—42no—
758C2×C3—82no—
759C2×C3—82no—
760C2×C3—81no—
761C2×C3—81no—
762C2×C3—241no—
763C2×C3C2×#93911yescharacteristic
764C2×C3C2×C3×#12111yescharacteristic
765D3—81no—
766C22—22no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—81no—
771C22—121no—
772C22—241no—
773C22C3×#93911yescharacteristic
774C22C3×#93911yescharacteristic
775C22C2×C3×#23711yescharacteristic
776C4—22no—
777C4—41no—
778C4—121no—
779C4C3×#93911yescharacteristic
780C4C3×#93911yescharacteristic
781C4C2×C3×D3×D411yescharacteristic
782C4C22×C3×#6711yescharacteristic
783C3—21no—
784C3#8400111yescharacteristic, direct product factor
785C3C3×#306711yescharacteristic, complemented
786C2—21no—
787C2—21no—
788C2—21no—
789C2—42no—
790C2—81no—
791C2—241no—
792C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC3×C4#939
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#575C2
socleC2×C32C2×#121
hypercenterC3×#575D3
hypocenterC3C3×#3067
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#575

Complements

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

NH ≅ G/Ntype
1. C32×#575C2semidirect
2. C3×#5822C2semidirect
3. C2×C3×#950C2semidirect
4. C2×C3×#948C2semidirect
5. C3×#5237C2semidirect
6. C3×#5204C2semidirect
7. C3×#5203C2semidirect
8. C3×#5200C2semidirect
9. C3×#5199C2semidirect
10. C3×#5132C2semidirect
11. C2×C3×#822C2semidirect
13. #84001C3direct (N × H)
34. C2×C3×#216C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#214C22semidirect
39. C2×C3×#213C22semidirect
45. C3×#836C22semidirect
46. C3×#833C22semidirect
47. C3×#824C22semidirect
48. C3×#823C22semidirect
49. C3×#822C22semidirect
50. C3×#822C22semidirect
53. C3×#575D3semidirect
54. C3×#575C2×C3semidirect
57. #5822C2×C3semidirect
58. C2×#950C2×C3semidirect
59. C2×#948C2×C3semidirect
67. #5237C2×C3semidirect
68. #5204C2×C3semidirect
69. #5203C2×C3semidirect
70. #5200C2×C3semidirect
71. #5199C2×C3semidirect
72. #5132C2×C3semidirect
73. C2×#822C2×C3semidirect
194. C2×#216C22×C3semidirect
196. C2×#215C22×C3semidirect
197. C2×#214C22×C3semidirect
199. C2×#213C22×C3semidirect
211. #836C22×C3semidirect
212. #833C22×C3semidirect
213. #824C22×C3semidirect
214. #823C22×C3semidirect
215. #822C22×C3semidirect
216. #822C22×C3semidirect
262. #575C3×D3semidirect
701. C32#3067semidirect
784. C3#84001direct (N × H)
785. C3C3×#3067semidirect

Maximal subgroups

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

subgroupindex
C32×#5752
C3×#58222
C2×C3×#9502
C2×C3×#9482
C3×#52372
C3×#52042
C3×#52032
C3×#52002
C3×#51992
C3×#51322
C2×C3×#8222
C3×#30673
#840013