Finite Group Databasebeta

← C2×#10591113 #11858163

Subgroups — C2×#10591113 #11858163

Order 1152.

1989 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4#10591113C218yesmaximal, direct product factor
5C2×#63570C214yesmaximal, complemented
6C2×#5139—31nomaximal
7C2×#5005—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×#638—21no—
10C2×#3828—21no—
11C2×#3828—22no—
12C2×#3828—21no—
13C2×#3828—22no—
14C2×#3828C412yescomplemented
15C2×#3828C414yescomplemented
16C2×#3828C2212yes—
17C2×#3828C2214yes—
18C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
19C22×C4×C3⋊D3—21no—
20C22×#634C411yescharacteristic, complemented
21C2×C3×#217—21no—
22C3×#926—22no—
23C3×#926C2214yescomplemented
24C2×C3×C4⋊Dic3—21no—
25C2×C3×C4×Dic3C2212yescomplemented
26C2×C3×#208—21no—
27C2×C3×#208—22no—
28C2×C3×#208C2212yescomplemented
29C2×C3×#208C2214yescomplemented
30C22×C3×C3⋊C8—21no—
31#63570C22116yescomplemented
32C22×#235—31no—
33C22×#235—31no—
34C22×#235—61no—
35C22×C3×M16—31no—
36C2×C3×#117—31no—
37C2×#926D311yescharacteristic, complemented
38C22×#208D311yescharacteristic, complemented
39#5139—38no—
40C2×#825—34no—
41#5005—38no—
42C2×#805—34no—
43C24×C32D411yescharacteristic
44C23×C3⋊D3—21no—
45C22×C32×C4C2×C411yescharacteristic
46C22×C32×C4C2×C411yescharacteristic
47C22×C32×C4C2×C412yes—
48C22×C32×C4D411yescharacteristic
49C22×C32×C4D412yes—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D412yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2312yes—
55C2×#638—22no—
56C2×#638—24no—
57C2×#638—22no—
58C2×#638—24no—
59C22×C3⋊Dic3—21no—
60#3828—24no—
61#3828—24no—
62#3828—24no—
63#3828—22no—
64#3828—22no—
65#3828—24no—
66#3828—24no—
67#3828C2×C414yes—
68#3828C2×C418yescomplemented
69#3828C2314yes—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)C2×C412yes—
73C2×C4⋊(C3⋊D3)C2×C414yescomplemented
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3—24no—
78C2×#634—22no—
79C2×#634—21no—
80C2×#634C2×C412yes—
81C2×#634C2×C414yescomplemented
82C22×C3×Dic3—22no—
83C3×#217—24no—
84C3×C4⋊Dic3—24no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2314yescomplemented
87C3×#208—24no—
88C3×#208—22no—
89C3×#208C2314yescomplemented
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8—24no—
92C2×#421—91noSylow
93C23×C3×C4—21no—
94C23×C3×C4C2×D311yescharacteristic
95C23×C3×C4C2×D311yescharacteristic
96C22×#67—62no—
97C22×#67—61no—
98C22×#67—61no—
99C2×#235—32no—
100C2×#235—32no—
101C2×#235—34no—
102C2×#235—34no—
103C2×#235—32no—
104C2×#235—34no—
105C2×#235—32no—
106C2×#235—34no—
107C2×#235—62no—
108C2×#235—64no—
109C2×#235—62no—
110C2×#235—64no—
111C2×#235—62no—
112C2×#235—64no—
113C2×#235—64no—
114C2×#235—62no—
115C2×#235—61no—
116C2×#235—62no—
117C2×#235—61no—
118C2×#235—62no—
119C2×#235—61no—
120C2×#235—62no—
121C2×#235—61no—
122C2×#235—62no—
123C22×D12—31no—
124C22×D12—31no—
125C22×D12—61no—
126C22×C4×D3—62no—
127C22×C4×D3—61no—
128C22×C4×D3—61no—
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—61no—
132C2×C3×M16—32no—
133C2×C3×M16—34no—
134C2×C3×M16—61no—
135C2×C3×M16—62no—
136C22×C3×C8—61no—
137C3×#117—34no—
138C3×#117—62no—
139C2×C3×C4⋊C4—61no—
140C2×C3×C22⋊C4—61no—
141C2×C3×C42—32no—
142C2×#217—21no—
143#926—22no—
144#926C2×D314yescomplemented
145C2×C4⋊Dic3—21no—
146C2×C4×Dic3C2×D312yescomplemented
147C2×#208—21no—
148C2×#208—22no—
149C2×#208C2×D312yescomplemented
150C2×#208C2×D314yescomplemented
151C22×C3⋊C8—21no—
152#825—316no—
153#805—316no—
154C23×C32—42no—
155C23×C32C22⋊C411yescharacteristic
156C23×C32C22⋊C411yescharacteristic
157C23×C32C22⋊C412yes—
158C23×C32C2×D411yescharacteristic
159C23×C32C2×D412yes—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—24no—
162C22×C3⋊D3—44no—
163C2×C32×C4C22⋊C412yes—
164C2×C32×C4C22⋊C411yescharacteristic
165C2×C32×C4C22⋊C412yes—
166C2×C32×C4C22⋊C411yescharacteristic
167C2×C32×C4C22⋊C412yes—
168C2×C32×C4C22⋊C412yes—
169C2×C32×C4C22⋊C412yes—
170C2×C32×C4C22×C411yescharacteristic
171C2×C32×C4C22×C412yes—
172C2×C32×C4C22×C411yescharacteristic
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181#638—24no—
182#638—28no—
183#638—24no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—24no—
186C4⋊(C3⋊D3)—22no—
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)C22×C414yes—
189C4×C3⋊D3—24no—
190C4×C3⋊D3—28no—
191C4×C3⋊D3—24no—
192#634—22no—
193#634—24no—
194#634C22×C414yes—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—44no—
197C3×C3⋊C8—24no—
198C22×#41—91no—
199C22×M16—31no—
200C2×#117—31no—
201#421—98no—
202C2×#104—94no—
203C24×C3—21no—
204C24×C3D1211yescharacteristic
205C24×C3#6711yescharacteristic
206C23×D3—62no—
207C23×D3—61no—
208C23×D3—61no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—62no—
220C22×C3×C4C4×D311yescharacteristic
221C22×C3×C4C4×D311yescharacteristic
222C22×C3×C4C4×D311yescharacteristic
223C22×C3×C4C4×D311yescharacteristic
224C22×C3×C4C4×D312yes—
225C22×C3×C4C4×D312yes—
226C22×C3×C4D1211yescharacteristic
227C22×C3×C4D1212yes—
228C22×C3×C4D1211yescharacteristic
229C22×C3×C4D1211yescharacteristic
230C22×C3×C4D1212yes—
231C22×C3×C4#6711yescharacteristic
232C22×C3×C4#6712yes—
233C22×C3×C4#6711yescharacteristic
234C22×C3×C4#6711yescharacteristic
235C22×C3×C4#6712yes—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D312yes—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D312yes—
240C2×#67—64no—
241C2×#67—68no—
242C2×#67—64no—
243C2×#67—68no—
244C2×#67—62no—
245C2×#67—62no—
246C2×#67—64no—
247C2×#67—64no—
248C2×#67—62no—
249C2×#67—64no—
250C2×#67—62no—
251C2×#67—64no—
252C22×Dic3—22no—
253C22×Dic3—62no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256#235—34no—
257#235—34no—
258#235—38no—
259#235—38no—
260#235—34no—
261#235—34no—
262#235—64no—
263#235—68no—
264#235—64no—
265#235—68no—
266#235—68no—
267#235—68no—
268#235—68no—
269#235—64no—
270#235—64no—
271#235—68no—
272#235—64no—
273#235—64no—
274#235—64no—
275#235—64no—
276#235—64no—
277#235—64no—
278#235—62no—
279#235—64no—
280#235—64no—
281#235—62no—
282#235—62no—
283#235—64no—
284#235—64no—
285#235—62no—
286C2×D12—32no—
287C2×D12—32no—
288C2×D12—34no—
289C2×D12—34no—
290C2×D12—62no—
291C2×D12—64no—
292C2×D12—64no—
293C2×D12—62no—
294C2×D12—62no—
295C2×D12—62no—
296C2×D12—61no—
297C2×D12—61no—
298C2×C4×D3—68no—
299C2×C4×D3—64no—
300C2×C4×D3—68no—
301C2×C4×D3—64no—
302C2×C4×D3—64no—
303C2×C4×D3—62no—
304C2×C4×D3—64no—
305C2×C4×D3—62no—
306C2×C4×D3—64no—
307C2×C4×D3—62no—
308C2×C4×D3—64no—
309C2×C4×D3—62no—
310C2×Dic6—32no—
311C2×Dic6—32no—
312C2×Dic6—34no—
313C2×Dic6—34no—
314C2×Dic6—62no—
315C2×Dic6—64no—
316C2×Dic6—64no—
317C2×Dic6—62no—
318C2×Dic6—62no—
319C2×Dic6—62no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C3×M16—34no—
323C3×M16—64no—
324C3×M16—62no—
325C2×C3×C8—64no—
326C2×C3×C8—62no—
327C3×C4⋊C4—64no—
328C3×C22⋊C4—64no—
329C3×C42—34no—
330C3×C42—62no—
331#217—24no—
332C4⋊Dic3—24no—
333C4×Dic3—22no—
334C4×Dic3C22×D314yescomplemented
335#208—24no—
336#208—22no—
337#208C22×D314yescomplemented
338C2×C3⋊C8—24no—
339C2×C3⋊C8—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—42no—
344C22×C32—42no—
345C22×C32C2×C22⋊C412yes—
346C22×C32C2×C22⋊C411yescharacteristic
347C22×C32C2×C22⋊C412yes—
348C22×C32C2×C22⋊C411yescharacteristic
349C22×C32C22×D411yescharacteristic
350C2×C3⋊D3—24no—
351C2×C3⋊D3—48no—
352C2×C3⋊D3—44no—
353C32×C4C2×C22⋊C411yescharacteristic
354C32×C4C2×C22⋊C412yes—
355C32×C4C2×C22⋊C411yescharacteristic
356C32×C4C2×C22⋊C412yes—
357C32×C4C23×C411yescharacteristic
358C32×C4C22×D411yescharacteristic
359C3⋊Dic3—24no—
360C3×Dic3—44no—
361C2×#41—92no—
362C2×#41—94no—
363C2×#41—92no—
364C2×#41—94no—
365C2×#41—181no—
366C2×#41—182no—
367C2×#41—182no—
368C2×#41—181no—
369C22×Q8—91no—
370C22×D4—91no—
371C22×D4—181no—
372C23×C4—181no—
373C23×C4D3211yescharacteristic
374C2×M16—32no—
375C2×M16—34no—
376C2×M16—62no—
377C2×M16—61no—
378C22×C8—61no—
379#117—34no—
380#117—62no—
381C2×C4⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C42—32no—
384#104—916no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—21no—
389C23×C3—22no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—44no—
393C23×C3(C2×D3)⋊C411yescharacteristic
394C23×C3(C2×D3)⋊C411yescharacteristic
395C23×C3(C2×D3)⋊C411yescharacteristic
396C23×C3(C2×D3)⋊C411yescharacteristic
397C23×C3(C2×D3)⋊C412yes—
398C23×C3(C2×D3)⋊C412yes—
399C23×C3C2×D1211yescharacteristic
400C23×C3C2×D1212yes—
401C23×C3C2×#6711yescharacteristic
402C23×C3C2×#6712yes—
403C22×D3—64no—
404C22×D3—68no—
405C22×D3—64no—
406C22×D3—64no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—128no—
410C22×D3—124no—
411C22×D3—124no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—64no—
431C2×C3×C4—124no—
432C2×C3×C4(C2×D3)⋊C412yes—
433C2×C3×C4(C2×D3)⋊C412yes—
434C2×C3×C4(C2×D3)⋊C411yescharacteristic
435C2×C3×C4(C2×D3)⋊C411yescharacteristic
436C2×C3×C4(C2×D3)⋊C412yes—
437C2×C3×C4(C2×D3)⋊C412yes—
438C2×C3×C4(C2×D3)⋊C411yescharacteristic
439C2×C3×C4(C2×D3)⋊C411yescharacteristic
440C2×C3×C4(C2×D3)⋊C412yes—
441C2×C3×C4(C2×D3)⋊C412yes—
442C2×C3×C4(C2×D3)⋊C412yes—
443C2×C3×C4(C2×D3)⋊C412yes—
444C2×C3×C4(C2×D3)⋊C412yes—
445C2×C3×C4(C2×D3)⋊C412yes—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4C2×C4×D312yes—
448C2×C3×C4C2×C4×D311yescharacteristic
449C2×C3×C4C2×C4×D311yescharacteristic
450C2×C3×C4C2×C4×D311yescharacteristic
451C2×C3×C4C2×C4×D312yes—
452C2×C3×C4C2×C4×D311yescharacteristic
453C2×C3×C4C2×C4×D312yes—
454C2×C3×C4C2×D1211yescharacteristic
455C2×C3×C4C2×D1212yes—
456C2×C3×C4C2×D1212yes—
457C2×C3×C4C2×D1212yes—
458C2×C3×C4C2×D1211yescharacteristic
459C2×C3×C4C2×D1211yescharacteristic
460C2×C3×C4C2×#6711yescharacteristic
461C2×C3×C4C2×#6712yes—
462C2×C3×C4C2×#6712yes—
463C2×C3×C4C2×#6712yes—
464C2×C3×C4C2×#6711yescharacteristic
465C2×C3×C4C2×#6711yescharacteristic
466C2×C3×C4C23×D311yescharacteristic
467C2×C3×C4C23×D311yescharacteristic
468#67—68no—
469#67—68no—
470#67—616no—
471#67—64no—
472#67—68no—
473#67—64no—
474#67—68no—
475#67—64no—
476#67—64no—
477C2×Dic3—24no—
478C2×Dic3—44no—
479C2×Dic3—64no—
480C2×Dic3—68no—
481C2×Dic3—64no—
482C2×Dic3—64no—
483C2×Dic3—62no—
484C2×Dic3—62no—
485D12—34no—
486D12—34no—
487D12—64no—
488D12—64no—
489D12—68no—
490D12—62no—
491D12—62no—
492D12—64no—
493D12—64no—
494C4×D3—68no—
495C4×D3—68no—
496C4×D3—616no—
497C4×D3—64no—
498C4×D3—64no—
499C4×D3—68no—
500C4×D3—68no—
501C4×D3—64no—
502C4×D3—64no—
503Dic6—34no—
504Dic6—34no—
505Dic6—64no—
506Dic6—64no—
507Dic6—68no—
508Dic6—62no—
509Dic6—62no—
510Dic6—64no—
511Dic6—64no—
512C3×C8—64no—
513C3⋊C8—24no—
514C2×C32—22no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—22no—
518C2×C32#42112yescomplemented
519C2×C32C22×C22⋊C411yescharacteristic
520C3⋊D3—44no—
521C24—181no—
522C24#62611yescharacteristic
523#41—94no—
524#41—94no—
525#41—98no—
526#41—184no—
527#41—184no—
528#41—184no—
529#41—184no—
530#41—182no—
531#41—182no—
532#41—184no—
533C2×Q8—92no—
534C2×Q8—94no—
535C2×Q8—182no—
536C2×Q8—181no—
537C2×D4—92no—
538C2×D4—94no—
539C2×D4—182no—
540C2×D4—184no—
541C2×D4—182no—
542C2×D4—184no—
543C2×D4—182no—
544C2×D4—181no—
545C22×C4—62no—
546C22×C4—181no—
547C22×C4—184no—
548C22×C4—182no—
549C22×C4—184no—
550C22×C4—182no—
551C22×C4#62411yescharacteristic
552C22×C4#62411yescharacteristic
553C22×C4#62412yes—
554C22×C4#62611yescharacteristic
555C22×C4#62612yes—
556C22×C4#62612yes—
557C22×C4#62611yescharacteristic
558C22×C4#62611yescharacteristic
559C22×C4C2×D3212yes—
560C22×C4C2×D3211yescharacteristic
561M16—34no—
562M16—64no—
563M16—62no—
564C2×C8—64no—
565C2×C8—62no—
566C4⋊C4—64no—
567C22⋊C4—64no—
568C42—34no—
569C42—62no—
570C22×C3—24no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—21no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—22no—
581C22×C3—21no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3C2×(C2×D3)⋊C412yes—
591C22×C3C2×(C2×D3)⋊C412yes—
592C22×C3C2×(C2×D3)⋊C412yes—
593C22×C3C2×(C2×D3)⋊C411yescharacteristic
594C22×C3C2×(C2×D3)⋊C412yes—
595C22×C3C2×(C2×D3)⋊C411yescharacteristic
596C22×C3C2×(C2×D3)⋊C411yescharacteristic
597C22×C3C2×(C2×D3)⋊C411yescharacteristic
598C22×C3C22×D1211yescharacteristic
599C22×C3C22×#6711yescharacteristic
600C2×D3—68no—
601C2×D3—64no—
602C2×D3—64no—
603C2×D3—1216no—
604C2×D3—128no—
605C2×D3—128no—
606C2×D3—128no—
607C2×D3—124no—
608C2×D3—124no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—22no—
612C3×C4—21no—
613C3×C4—22no—
614C3×C4—21no—
615C3×C4—124no—
616C3×C4C2×(C2×D3)⋊C412yes—
617C3×C4C2×(C2×D3)⋊C411yescharacteristic
618C3×C4C2×(C2×D3)⋊C411yescharacteristic
619C3×C4C2×(C2×D3)⋊C412yes—
620C3×C4C2×(C2×D3)⋊C412yes—
621C3×C4C2×(C2×D3)⋊C412yes—
622C3×C4C2×(C2×D3)⋊C411yescharacteristic
623C3×C4C2×(C2×D3)⋊C411yescharacteristic
624C3×C4C22×C4×D311yescharacteristic
625C3×C4C22×C4×D311yescharacteristic
626C3×C4C22×D1211yescharacteristic
627C3×C4C22×#6711yescharacteristic
628Dic3—44no—
629Dic3—68no—
630Dic3—64no—
631Dic3—64no—
632C32C2×#42111yescharacteristic, complemented, Sylow
633C23—42no—
634C23—184no—
635C23—182no—
636C23—364no—
637C23#372211yescharacteristic
638C23#372211yescharacteristic
639C23#372212yes—
640C23C2×#62611yescharacteristic
641C23C2×#62612yes—
642Q8—94no—
643Q8—184no—
644Q8—182no—
645D4—94no—
646D4—184no—
647D4—188no—
648D4—184no—
649D4—184no—
650D4—182no—
651C2×C4—64no—
652C2×C4—124no—
653C2×C4—184no—
654C2×C4—182no—
655C2×C4—184no—
656C2×C4—188no—
657C2×C4—184no—
658C2×C4#372211yescharacteristic
659C2×C4#372212yes—
660C2×C4#372212yes—
661C2×C4#372211yescharacteristic
662C2×C4#372212yes—
663C2×C4#372212yes—
664C2×C4#372212yes—
665C2×C4C2×#62412yes—
666C2×C4C2×#62411yescharacteristic
667C2×C4C2×#62412yes—
668C2×C4C2×#62411yescharacteristic
669C2×C4C2×#62612yes—
670C2×C4C2×#62612yes—
671C2×C4C2×#62611yescharacteristic
672C2×C4C2×#62611yescharacteristic
673C2×C4C2×#62612yes—
674C2×C4C2×#62611yescharacteristic
675C2×C4C22×D3211yescharacteristic
676C8—64no—
677C2×C3—24no—
678C2×C3—21no—
679C2×C3—22no—
680C2×C3—21no—
681C2×C3—22no—
682C2×C3—21no—
683C2×C3—22no—
684C2×C3—21no—
685C2×C3—22no—
686C2×C3—22no—
687C2×C3—21no—
688C2×C3—41no—
689C2×C3—41no—
690C2×C3—42no—
691C2×C3#500512yescomplemented
692C2×C3#513912yescomplemented
693C2×C3C22×(C2×D3)⋊C411yescharacteristic
694C2×C3C22×(C2×D3)⋊C411yescharacteristic
695D3—128no—
696D3—124no—
697D3—124no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—42no—
702C22—42no—
703C22—184no—
704C22—368no—
705C22—364no—
706C22C2×#372212yes—
707C22C2×#372212yes—
708C22C2×#372211yescharacteristic
709C22C2×#372211yescharacteristic
710C22C22×#62611yescharacteristic
711C4—124no—
712C4—184no—
713C4C2×#372212yes—
714C4C2×#372211yescharacteristic
715C4C2×#372212yes—
716C4C2×#372211yescharacteristic
717C4C22×#62411yescharacteristic
718C4C22×#62611yescharacteristic
719C3—21no—
720C3C2×#500511yescharacteristic, complemented
721C3C2×#513911yescharacteristic, complemented
722C2—21no—
723C2—22no—
724C2—21no—
725C2—22no—
726C2—364no—
727C2#1059111312yesdirect product factor
728C2C22×#372211yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3828C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C22×C3×#208C2semidirect
4. #10591113C2direct (N × H)
5. C2×#63570C2semidirect
14. C2×#3828C4semidirect
15. C2×#3828C4semidirect
18. C22×C4⋊(C3⋊D3)C4semidirect
20. C22×#634C4semidirect
23. C3×#926C22semidirect
25. C2×C3×C4×Dic3C22semidirect
28. C2×C3×#208C22semidirect
29. C2×C3×#208C22semidirect
31. #63570C22semidirect
37. C2×#926D3semidirect
38. C22×#208D3semidirect
68. #3828C2×C4semidirect
73. C2×C4⋊(C3⋊D3)C2×C4semidirect
81. C2×#634C2×C4semidirect
86. C3×C4×Dic3C23semidirect
89. C3×#208C23semidirect
144. #926C2×D3semidirect
146. C2×C4×Dic3C2×D3semidirect
149. C2×#208C2×D3semidirect
150. C2×#208C2×D3semidirect
334. C4×Dic3C22×D3semidirect
337. #208C22×D3semidirect
518. C2×C32#421semidirect
632. C32C2×#421semidirect
691. C2×C3#5005semidirect
692. C2×C3#5139semidirect
720. C3C2×#5005semidirect
721. C3C2×#5139semidirect
727. C2#10591113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9262
C22×C3×#2082
#105911132
C2×#635702
C2×#51393
C2×#50053