Finite Group Databasebeta

← C3×#79496 #11884238

Subgroups — C3×#79496 #11884238

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3C3×#5551C211yesmaximal, characteristic, complemented
4C3×#5550C211yesmaximal, characteristic, complemented
5C32×#435C211yesmaximal, characteristic, complemented
6C3×#5137C211yesmaximal, characteristic, complemented
7C3×#5114C211yesmaximal, characteristic, complemented
8C3×#4844C211yesmaximal, characteristic, complemented
9C3×#4841C211yesmaximal, characteristic, complemented
10C3×#4734C211yesmaximal, characteristic, complemented
11C3×#4733C211yesmaximal, characteristic, complemented
12C3×#4733C211yesmaximal, characteristic, complemented
13C3×#4731C211yesmaximal, characteristic, complemented
14C3×#4715C211yesmaximal, characteristic, complemented
15C3×#4711C211yesmaximal, characteristic, complemented
16C3×#3267—31nomaximal
17#79496C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C2×C32×M16C2211yescharacteristic
23C22×C32×C8C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic
25C3×#938—21no—
26C3×#937—21no—
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C3×#908—24no—
32C2×C3×Dic12C2211yescharacteristic, complemented
33C2×C3×Dic12C2211yescharacteristic, complemented
34C3×#904—24no—
35C2×C3×D24C2211yescharacteristic
36C2×C3×D24C2211yescharacteristic
37C2×C3×#204C2211yescharacteristic
38C2×C3×#204C2211yescharacteristic
39C2×C3×#204C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic
41C2×C3×#204C2211yescharacteristic, complemented
42C3×#894—21no—
43C3×D3×C4⋊C4—21no—
44C3×#884—21no—
45C3×#883—21no—
46C3×#883—21no—
47C3×D3×C22⋊C4—21no—
48C3×#875C2211yescharacteristic
49C3×C4×D12C2211yescharacteristic
50C3×C4×D12C2211yescharacteristic, complemented
51C3×#869C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×C22⋊C8C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic, complemented
55C32×#97C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic
58C3×#821C2211yescharacteristic, complemented
59C3×#817C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#816C2211yescharacteristic, complemented
62C3×#816C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#547—31no—
66C3×#546—31no—
67C2×#908C2×C311yescharacteristic, complemented
68C2×#904C2×C311yescharacteristic, complemented
69#5551C2×C311yescharacteristic, complemented
70#5550C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#470—31no—
73C3×#465—31no—
74C3×#463—31no—
75C3×#461—31no—
76C3×#452—31no—
77C3×#452—31no—
78C3×#450—31no—
79C3×#449—31no—
80C3×#442—31no—
81C3×#435—21no—
82C3×#435D311yescharacteristic, complemented
83C3×#435C2×C311yescharacteristic, complemented
84#5137C2×C311yescharacteristic, complemented
85#5114C2×C311yescharacteristic, complemented
86#4844C2×C311yescharacteristic, complemented
87#4841C2×C311yescharacteristic, complemented
88#4734C2×C311yescharacteristic, complemented
89#4733C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic, complemented
91#4731C2×C311yescharacteristic, complemented
92#4715C2×C311yescharacteristic, complemented
93#4711C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×D4D411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×#235—22no—
103C3×#235—22no—
104C3×#235—22no—
105C3×#235—41no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12—22no—
109C2×C3×D12—21no—
110C2×C3×D12—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C32×M16—22no—
123C2×C32×C8—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4D411yescharacteristic
129C32×C22⋊C4D411yescharacteristic
130C32×C22⋊C4D411yescharacteristic
131C32×C42C2311yescharacteristic
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic12—22no—
148C3×Dic12—41no—
149C3×D24—22no—
150C3×D24D414yescomplemented
151C3×#204—22no—
152C3×#204—22no—
153C3×#204—22no—
154C3×#204—22no—
155C3×#204—41no—
156#3267—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#235C22×C311yescharacteristic
162C2×#235C22×C311yescharacteristic
163C2×#235C22×C311yescharacteristic, complemented
164C22×D12C22×C311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×M16—21no—
177C2×C3×M16C2×D311yescharacteristic
178C2×C3×M16C22×C311yescharacteristic
179C22×C3×C8—21no—
180C22×C3×C8C2×D311yescharacteristic, complemented
181C22×C3×C8C22×C311yescharacteristic, complemented
182C3×C4⋊Q8—31no—
183C3×#124—31no—
184C3×#123—61no—
185C3×#123—61no—
186C3×#123—61no—
187C3×C22⋊Q8—31no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—31no—
190C3×#121—31no—
191C3×#121—61no—
192C3×#121—61no—
193C3×#120—61no—
194C3×C4×D4—21no—
195C3×C4×D4—31no—
196C3×C4×D4—31no—
197C3×C4×D4C2×D311yescharacteristic
198C3×C4×D4C22×C311yescharacteristic
199C2×C3×C4⋊C4—61no—
200C2×C3×C22⋊C4—61no—
201#938—21no—
202#937—21no—
203#930C22×C311yescharacteristic
204#924C22×C311yescharacteristic
205#924C22×C311yescharacteristic
206#924C22×C311yescharacteristic, complemented
207#908—24no—
208C2×Dic12C22×C311yescharacteristic, complemented
209C2×Dic12C22×C311yescharacteristic, complemented
210#904—24no—
211C2×D24C22×C311yescharacteristic
212C2×D24C22×C311yescharacteristic
213C2×#204C22×C311yescharacteristic
214C2×#204C22×C311yescharacteristic
215C2×#204C22×C311yescharacteristic
216C2×#204C22×C311yescharacteristic
217C2×#204C22×C311yescharacteristic, complemented
218#894—21no—
219D3×C4⋊C4—21no—
220#884—21no—
221#883—21no—
222#883—21no—
223D3×C22⋊C4—21no—
224#875C22×C311yescharacteristic
225C4×D12C22×C311yescharacteristic
226C4×D12C22×C311yescharacteristic, complemented
227#869C22×C311yescharacteristic, complemented
228C3×#106—31no—
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C22×C311yescharacteristic, complemented
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×C22⋊C8—21no—
239C3×C22⋊C8—21no—
240C3×C22⋊C8C2×D311yescharacteristic
241C3×C22⋊C8C2×D311yescharacteristic, complemented
242C3×C22⋊C8C22×C311yescharacteristic
243C3×C22⋊C8C22×C311yescharacteristic, complemented
244C3×#97—21no—
245C3×#97C2×D311yescharacteristic, complemented
246C3×#97C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic
248#821C22×C311yescharacteristic
249#821C22×C311yescharacteristic, complemented
250#817C22×C311yescharacteristic, complemented
251#816C22×C311yescharacteristic, complemented
252#816C22×C311yescharacteristic, complemented
253#816C22×C311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C32×D4—41no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—81no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—42no—
286C3×D12C2×D412yes—
287C3×D12C2×D412yes—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—81no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C32×C8—21no—
300C32×C8—21no—
301C32×C8—21no—
302C32×C8C2×D412yes—
303C2×AGL(1,ℤ/8)—31no—
304C2×#135—31no—
305#547—31no—
306#546—31no—
307#497—31no—
308#470—31no—
309#465—31no—
310#463—31no—
311#461—31no—
312#452—31no—
313#452—31no—
314#450—31no—
315#449—31no—
316#442—31no—
317#435C3×D311yescharacteristic, complemented
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—121no—
340C2×C3×D4D1211yescharacteristic
341C2×C3×D4C3×D411yescharacteristic
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C23×C311yescharacteristic
352C22×C3×C4C23×C311yescharacteristic
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357#235—22no—
358#235—22no—
359#235—22no—
360#235—41no—
361#235—41no—
362#235—41no—
363C2×D12—22no—
364C2×D12—21no—
365C2×D12—41no—
366C2×D12C23×C311yescharacteristic
367C2×D12C23×C311yescharacteristic
368C2×D12C23×C311yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×Dic6C23×C311yescharacteristic
375C2×Dic6C23×C311yescharacteristic
376C2×Dic6C23×C311yescharacteristic
377C3×Q16—62no—
378C3×Q16—121no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×SD16—121no—
384C3×D8—34no—
385C3×D8—62no—
386C3×M16—22no—
387C3×M16—22no—
388C3×M16—42no—
389C2×C3×C8—22no—
390C2×C3×C8—22no—
391C2×C3×C8—21no—
392C2×C3×C8—21no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—42no—
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C23×C311yescharacteristic
401C2×C3×C8C23×C311yescharacteristic
402C2×C3×C8C23×C311yescharacteristic
403C2×C3×C8C23×C311yescharacteristic
404C3×C4⋊C4—21no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4D1211yescharacteristic
413C3×C4⋊C4C3×D411yescharacteristic
414C3×C22⋊C4—21no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C22⋊C4—61no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4D1211yescharacteristic
425C3×C22⋊C4D1211yescharacteristic
426C3×C22⋊C4C3×D411yescharacteristic
427C3×C22⋊C4C3×D411yescharacteristic
428C3×C42—21no—
429C3×C42C22×D311yescharacteristic
430C3×C42C23×C311yescharacteristic
431#217—21no—
432#217—21no—
433#217—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439C4⋊Dic3—21no—
440C4⋊Dic3—21no—
441C4⋊Dic3C23×C311yescharacteristic
442C4⋊Dic3C23×C311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445Dic3⋊C4—21no—
446Dic12—22no—
447Dic12—41no—
448D24—22no—
449D24C3×D414yescomplemented
450#204—22no—
451#204—22no—
452#204—22no—
453#204—22no—
454#204—41no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—31no—
486C22×D4—31no—
487AGL(1,ℤ/8)—64no—
488#135—64no—
489C2×Q16—31no—
490C2×Q16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—31no—
496C2×D8—31no—
497C2×D8—31no—
498C2×M16C2×C3×D311yescharacteristic
499C22×C8C2×C3×D311yescharacteristic, complemented
500C4⋊Q8—31no—
501#124—31no—
502#123—61no—
503#123—61no—
504#123—61no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507C22⋊Q8—31no—
508#121—31no—
509#121—61no—
510#121—61no—
511#120—61no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4C2×C3×D311yescharacteristic
515C2×C4⋊C4—61no—
516C2×C22⋊C4—61no—
517#106—31no—
518C4⋊C8C2×C3×D311yescharacteristic, complemented
519#103—31no—
520#103—31no—
521#103—31no—
522#102—31no—
523#102—31no—
524#102—31no—
525C22⋊C8C2×C3×D311yescharacteristic
526C22⋊C8C2×C3×D311yescharacteristic, complemented
527#97C2×C3×D311yescharacteristic, complemented
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—241no—
536C23×C3C2×D1211yescharacteristic
537C23×C3C2×D1211yescharacteristic
538C23×C3C2×C3×D411yescharacteristic
539C23×C3C2×C3×D411yescharacteristic
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—81no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×D4—32no—
553C3×D4—32no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—42no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—122no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4—241no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4—122no—
591C2×C3×C4—122no—
592C2×C3×C4—241no—
593C2×C3×C4C2×D1211yescharacteristic
594C2×C3×C4C2×D1211yescharacteristic
595C2×C3×C4C2×D1211yescharacteristic
596C2×C3×C4C2×D1211yescharacteristic
597C2×C3×C4C2×C3×D411yescharacteristic
598C2×C3×C4C2×C3×D411yescharacteristic
599C2×C3×C4C2×C3×D411yescharacteristic
600C2×C3×C4C2×C3×D411yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C24×C311yescharacteristic
603#67—42no—
604#67—42no—
605#67—42no—
606#67—81no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12C2×C3×D412yes—
618D12C2×C3×D412yes—
619C4×D3—42no—
620C4×D3—42no—
621C4×D3—42no—
622C4×D3—42no—
623C4×D3—81no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630C3×C8—21no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—22no—
637C3×C8—41no—
638C3×C8—41no—
639C3×C8—41no—
640C3×C8D3×D412yes—
641C3×C8C2×C3×D412yes—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32D4211yescharacteristic
645C2×C32#57511yescharacteristic
646C2×C32#57711yescharacteristic
647C3×D3—42no—
648C3×D3—42no—
649C3×D3—81no—
650C24—61no—
651#41—62no—
652#41—62no—
653#41—62no—
654#41—121no—
655#41—121no—
656#41—121no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—121no—
670C2×D4C3×D1211yescharacteristic
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4C22×C3×D311yescharacteristic
677C22×C4C22×C3×D311yescharacteristic
678Q16—62no—
679Q16—121no—
680SD16—62no—
681SD16—62no—
682SD16—62no—
683SD16—62no—
684SD16—121no—
685D8—34no—
686D8—62no—
687M16—22no—
688C2×C8—22no—
689C2×C8C22×C3×D311yescharacteristic
690C2×C8C22×C3×D311yescharacteristic
691C2×C8C22×C3×D311yescharacteristic
692C2×C8C22×C3×D311yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4C3×D1211yescharacteristic
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4C3×D1211yescharacteristic
710C22⋊C4C3×D1211yescharacteristic
711C42C22×C3×D311yescharacteristic
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—244no—
741C22×C3C22×D1211yescharacteristic
742C22×C3C22×C3×D411yescharacteristic
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—84no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4C2×D3×D411yescharacteristic
773C3×C4#100911yescharacteristic
774C3×C4C22×C3×D411yescharacteristic
775C3×C4C3×H(5,𝔽2)11yescharacteristic
776Dic3—41no—
777Dic3—41no—
778Dic3—41no—
779Dic3—41no—
780Dic3—41no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—61no—
783C23—61no—
784C23—61no—
785C23—122no—
786C23—122no—
787C23—241no—
788C23C2×C3×D1211yescharacteristic
789C23C2×C3×D1211yescharacteristic
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—32no—
797D4—32no—
798D4—41no—
799D4—61no—
800D4—61no—
801D4—61no—
802D4—61no—
803D4—122no—
804D4—122no—
805D4—122no—
806D4—122no—
807D4—241no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—241no—
822C2×C4C2×C3×D1211yescharacteristic
823C2×C4C2×C3×D1211yescharacteristic
824C2×C4C2×C3×D1211yescharacteristic
825C2×C4C2×C3×D1211yescharacteristic
826C2×C4C23×C3×D311yescharacteristic
827C8—21no—
828C8—21no—
829C8—21no—
830C8C3×D3×D412yes—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—41no—
838C2×C3—41no—
839C2×C3—81no—
840C2×C3—122no—
841C2×C3—122no—
842C2×C3—241no—
843C2×C3D4×D1211yescharacteristic
844C2×C3#574811yescharacteristic
845C2×C3#575111yescharacteristic
846C2×C3C3×D4211yescharacteristic
847C2×C3C3×#57511yescharacteristic
848C2×C3C3×#57711yescharacteristic
849D3—42no—
850D3—42no—
851D3—81no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—62no—
859C22—62no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—244no—
868C22C22×C3×D1211yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—121no—
877C4—121no—
878C4C2×C3×D3×D411yescharacteristic
879C4C3×#100911yescharacteristic
880C3—21no—
881C3#7949611yescharacteristic, direct product factor
882C3C3×#326711yescharacteristic, complemented
883C2—41no—
884C2—41no—
885C2—122no—
886C2—122no—
887C2—241no—
888C2C3×D4×D1211yescharacteristic
889C2C3×#574811yescharacteristic
890C2C3×#575111yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#435C2
socleC22×C32C22×D4
hypercenterC3×#435D3
hypocenterC3C3×#3267
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. C2×C3×#904C2semidirect
3. C3×#5551C2semidirect
4. C3×#5550C2semidirect
5. C32×#435C2semidirect
6. C3×#5137C2semidirect
7. C3×#5114C2semidirect
8. C3×#4844C2semidirect
9. C3×#4841C2semidirect
10. C3×#4734C2semidirect
11. C3×#4733C2semidirect
12. C3×#4733C2semidirect
13. C3×#4731C2semidirect
14. C3×#4715C2semidirect
15. C3×#4711C2semidirect
17. #79496C3direct (N × H)
20. C2×C3×#235C22semidirect
23. C22×C32×C8C22semidirect
30. C3×#924C22semidirect
32. C2×C3×Dic12C22semidirect
33. C2×C3×Dic12C22semidirect
41. C2×C3×#204C22semidirect
50. C3×C4×D12C22semidirect
51. C3×#869C22semidirect
52. C32×C4⋊C8C22semidirect
54. C32×C22⋊C8C22semidirect
55. C32×#97C22semidirect
58. C3×#821C22semidirect
59. C3×#817C22semidirect
60. C3×#816C22semidirect
61. C3×#816C22semidirect
62. C3×#816C22semidirect
67. C2×#908C2×C3semidirect
68. C2×#904C2×C3semidirect
69. #5551C2×C3semidirect
70. #5550C2×C3semidirect
82. C3×#435D3semidirect
83. C3×#435C2×C3semidirect
84. #5137C2×C3semidirect
85. #5114C2×C3semidirect
86. #4844C2×C3semidirect
87. #4841C2×C3semidirect
88. #4734C2×C3semidirect
89. #4733C2×C3semidirect
90. #4733C2×C3semidirect
91. #4731C2×C3semidirect
92. #4715C2×C3semidirect
93. #4711C2×C3semidirect
150. C3×D24D4semidirect
163. C2×#235C22×C3semidirect
180. C22×C3×C8C2×D3semidirect
181. C22×C3×C8C22×C3semidirect
206. #924C22×C3semidirect
208. C2×Dic12C22×C3semidirect
209. C2×Dic12C22×C3semidirect
217. C2×#204C22×C3semidirect
226. C4×D12C22×C3semidirect
227. #869C22×C3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C22×C3semidirect
241. C3×C22⋊C8C2×D3semidirect
243. C3×C22⋊C8C22×C3semidirect
245. C3×#97C2×D3semidirect
246. C3×#97C22×C3semidirect
249. #821C22×C3semidirect
250. #817C22×C3semidirect
251. #816C22×C3semidirect
252. #816C22×C3semidirect
253. #816C22×C3semidirect
317. #435C3×D3semidirect
449. D24C3×D4semidirect
499. C22×C8C2×C3×D3semidirect
518. C4⋊C8C2×C3×D3semidirect
526. C22⋊C8C2×C3×D3semidirect
527. #97C2×C3×D3semidirect
781. C32#3267semidirect
881. C3#79496direct (N × H)
882. C3C3×#3267semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×C3×#9042
C3×#55512
C3×#55502
C32×#4352
C3×#51372
C3×#51142
C3×#48442
C3×#48412
C3×#47342
C3×#47332
C3×#47312
C3×#47152
C3×#47112
C3×#32673
#794963