Finite Group Databasebeta

← C2×#22610914 #33090622

Subgroups — C2×#22610914 #33090622

Order 18688.

1698 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556568C211yesmaximal, characteristic
2C2×#17988445C211yesmaximal, characteristic
3C2×C22⋊C4×Dic73C211yesmaximal, characteristic
4#22610914C218yesmaximal, direct product factor
5C2×#17988354C211yesmaximal, characteristic
6C2×#17988353C211yesmaximal, characteristic
7C2×#17988353C211yesmaximal, characteristic
8C2×#342×C73C211yesmaximal, characteristic
9C23×Dic146C411yescharacteristic, complemented
10C24×Dic73C2211yescharacteristic
11C2×#14556568—21no—
12C2×#14556568—21no—
13C2×#14556568—21no—
14C2×#14556568—21no—
15C2×#14556568—22no—
16C2×#14556568—22no—
17C2×#14556568C414yescomplemented
18C2×#14556568C2214yes—
19C22×C4⋊Dic73C411yescharacteristic, complemented
20C22×#11924007—21no—
21C22×#11924007C411yescharacteristic, complemented
22C22×#11924007C411yescharacteristic, complemented
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C4×Dic73—21no—
27#17988445—22no—
28#17988445C2214yes—
29C22⋊C4×Dic73—22no—
30C22⋊C4×Dic73C2214yes—
31C2×#14556498—21no—
32C2×#14556498—21no—
33#17988354C2214yes—
34#17988353C2214yes—
35#17988353C2214yes—
36C22×C22⋊C4×C73C2211yescharacteristic
37C22×C22⋊C4×C73C2211yescharacteristic
38C22×C22⋊C4×C73C2211yescharacteristic
39#342×C73C2214yes—
40C22×Dic146—22no—
41C22×Dic146—21no—
42C22×Dic146—21no—
43C22×Dic146—44no—
44C22×Dic146C2×C414yescomplemented
45C23×Dic73—21no—
46C23×Dic73—21no—
47C23×Dic73—44no—
48C23×Dic73C2×C411yescharacteristic
49C23×Dic73C2×C411yescharacteristic
50C23×Dic73C2×C411yescharacteristic
51C23×Dic73C2×C411yescharacteristic
52C23×Dic73C2×C412yes—
53C23×Dic73D411yescharacteristic
54C23×Dic73D411yescharacteristic
55C23×Dic73D411yescharacteristic
56C23×Dic73D411yescharacteristic
57C23×Dic73D412yes—
58C23×Dic73D412yes—
59C23×Dic73C2312yes—
60#14556568—24no—
61#14556568—24no—
62#14556568—24no—
63#14556568—24no—
64#14556568—24no—
65#14556568—24no—
66#14556568—24no—
67#14556568—24no—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73—21no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73C2×C414yescomplemented
72C2×#11924007—22no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×#11924007—22no—
78C2×#11924007—24no—
79C2×#11924007—44no—
80C2×#11924007C2×C414yescomplemented
81C2×#11924007C2×C414yescomplemented
82C2×C22⋊Dic73—21no—
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73—22no—
89C2×C22⋊Dic73—22no—
90C2×C22⋊Dic73—22no—
91C2×C22⋊Dic73C2×C412yes—
92C2×C22⋊Dic73Q814yescomplemented
93C2×C22⋊Dic73C2312yes—
94C2×C22⋊Dic73C2312yes—
95C2×C22⋊Dic73C2312yes—
96C2×C4×Dic73—24no—
97C2×C4×Dic73—44no—
98#14556498—24no—
99#14556498—24no—
100C25×C73C2311yescharacteristic
101C23×C4×C73—21no—
102C23×C4×C73—21no—
103C23×C4×C73C2×C411yescharacteristic
104C23×C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—22no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73C2×C412yes—
115C2×C22⋊C4×C73Q814yescomplemented
116C2×C22⋊C4×C73C2312yes—
117C2×C22⋊C4×C73C2312yes—
118C2×C22⋊C4×C73C2312yes—
119C2×Dic146—24no—
120C2×Dic146—24no—
121C2×Dic146—44no—
122C2×Dic146—48no—
123C2×Dic146—44no—
124C2×Dic146—48no—
125C22×Dic73—24no—
126C22×Dic73—24no—
127C22×Dic73—24no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—24no—
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—44no—
136C22×Dic73—44no—
137C22×Dic73—44no—
138C22×Dic73—44no—
139C22×Dic73—42no—
140C22×Dic73—42no—
141C22×Dic73—42no—
142C22×Dic73—42no—
143C22×Dic73—42no—
144C22×Dic73—42no—
145C22×Dic73—42no—
146C22×Dic73—42no—
147C22×Dic73—42no—
148C22×Dic73—42no—
149C22×Dic73C22⋊C411yescharacteristic
150C22×Dic73C22⋊C411yescharacteristic
151C22×Dic73C22⋊C412yes—
152C22×Dic73C22⋊C411yescharacteristic
153C22×Dic73C22⋊C412yes—
154C22×Dic73C22⋊C412yes—
155C22×Dic73C22⋊C412yes—
156C22×Dic73C22⋊C412yes—
157C22×Dic73C22⋊C412yes—
158C22×Dic73C22⋊C411yescharacteristic
159C22×Dic73C22×C412yes—
160C22×Dic73C22×C412yes—
161C22×Dic73C22×C412yes—
162C22×Dic73C22×C412yes—
163C22×Dic73C2×D412yes—
164C22×Dic73C2×D412yes—
165C22×Dic73C2×D412yes—
166C22×Dic73C2×D412yes—
167C4⋊Dic73—24no—
168C4⋊Dic73—24no—
169#11924007—24no—
170#11924007—24no—
171#11924007—24no—
172#11924007—24no—
173#11924007—48no—
174C22⋊Dic73—22no—
175C22⋊Dic73—22no—
176C22⋊Dic73—24no—
177C22⋊Dic73—22no—
178C22⋊Dic73—22no—
179C22⋊Dic73—22no—
180C22⋊Dic73—22no—
181C22⋊Dic73—22no—
182C22⋊Dic73—42no—
183C22⋊Dic73C2×Q814yescomplemented
184C4×Dic73—48no—
185C24×C73—42no—
186C24×C73—42no—
187C24×C73C22×C411yescharacteristic
188C24×C73C22×C411yescharacteristic
189C24×C73C2×D411yescharacteristic
190C24×C73C2×D411yescharacteristic
191C24×C73C2×D411yescharacteristic
192C24×C73C2×D411yescharacteristic
193C24×C73C2×Q812yes—
194C24×C73C2×Q812yes—
195C24×C73#4112yes—
196C24×C73#4112yes—
197C24×C73C2411yescharacteristic
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—24no—
203C22×C4×C73—22no—
204C22×C4×C73—22no—
205C22×C4×C73—42no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—42no—
209C22×C4×C73—42no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73C22×C412yes—
213C22×C4×C73C22×C412yes—
214C22⋊C4×C73—22no—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—24no—
217C22⋊C4×C73—22no—
218C22⋊C4×C73—22no—
219C22⋊C4×C73—22no—
220C22⋊C4×C73—22no—
221C22⋊C4×C73—22no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73C2×Q814yescomplemented
224C23×C73—22no—
225C23×C73—22no—
226C23×C73—22no—
227C23×C73—22no—
228C23×C73—22no—
229C23×C73—22no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—44no—
237C23×C73—44no—
238C23×C73—44no—
239C23×C73—44no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73C2×C22⋊C411yescharacteristic
243C23×C73C2×C22⋊C411yescharacteristic
244C23×C73C2×C22⋊C411yescharacteristic
245C23×C73C2×C22⋊C411yescharacteristic
246C23×C73C4×Q812yes—
247C23×C73C4×Q812yes—
248C23×C73C4×Q812yes—
249C23×C73C4×Q812yes—
250C23×C73C22⋊Q812yes—
251C23×C73C22⋊Q812yes—
252C23×C73C22⋊Q812yes—
253C23×C73C22⋊Q812yes—
254C23×C73#12412yes—
255C23×C73#12412yes—
256C23×C73C4⋊Q812yes—
257C23×C73C4⋊Q812yes—
258C23×C73C23×C411yescharacteristic
259C23×C73C22×D411yescharacteristic
260C23×C73C22×D411yescharacteristic
261C23×C73C22×Q811yescharacteristic
262C23×C73C22×Q811yescharacteristic
263C23×C73C2×#4111yescharacteristic
264C23×C73C2×#4111yescharacteristic
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—24no—
268C2×C4×C73—42no—
269C2×C4×C73—48no—
270C2×C4×C73—42no—
271C2×C4×C73—42no—
272C2×C4×C73—42no—
273C2×C4×C73—42no—
274C2×C4×C73—42no—
275C2×C4×C73—42no—
276C2×C4×C73—42no—
277C2×C4×C73—42no—
278C2×C4×C73—42no—
279C2×C4×C73—42no—
280C2×C4×C73—84no—
281C2×Dic73—22no—
282C2×Dic73—22no—
283C2×Dic73—22no—
284C2×Dic73—24no—
285C2×Dic73—24no—
286C2×Dic73—24no—
287C2×Dic73—24no—
288C2×Dic73—24no—
289C2×Dic73—24no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—24no—
293C2×Dic73—42no—
294C2×Dic73—42no—
295C2×Dic73—42no—
296C2×Dic73—42no—
297C2×Dic73—42no—
298C2×Dic73—42no—
299C2×Dic73—42no—
300C2×Dic73—42no—
301C2×Dic73—48no—
302C2×Dic73—42no—
303C2×Dic73—42no—
304C2×Dic73—42no—
305C2×Dic73—42no—
306C2×Dic73—42no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—84no—
312C2×Dic73#9914yes—
313C2×Dic73C2×C22⋊C412yes—
314C2×Dic73C2×C22⋊C412yes—
315C2×Dic73C2×C22⋊C412yes—
316C2×Dic73C2×C22⋊C412yes—
317Dic146—48no—
318Dic146—48no—
319C22×C73—21no—
320C22×C73—21no—
321C22×C73—21no—
322C22×C73—21no—
323C22×C73—21no—
324C22×C73—21no—
325C22×C73—21no—
326C22×C73—21no—
327C22×C73—21no—
328C22×C73—21no—
329C22×C73—21no—
330C22×C73—21no—
331C22×C73—24no—
332C22×C73—24no—
333C22×C73—24no—
334C22×C73—24no—
335C22×C73—24no—
336C22×C73—24no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73#39112yes—
348C22×C73#39112yes—
349C22×C73#39112yes—
350C22×C73#39112yes—
351C22×C73C2×#9912yes—
352C22×C73#41012yes—
353C22×C73C22×C22⋊C411yescharacteristic
354C22×C73C2×C4×Q811yescharacteristic
355C22×C73C2×C4×Q811yescharacteristic
356C22×C73C2×C22⋊Q811yescharacteristic
357C22×C73C2×C22⋊Q811yescharacteristic
358C22×C73C2×#12411yescharacteristic
359C22×C73C2×C4⋊Q811yescharacteristic
360C4×C73—44no—
361C4×C73—42no—
362C4×C73—42no—
363C4×C73—82no—
364Dic73—22no—
365Dic73—22no—
366Dic73—22no—
367Dic73—44no—
368Dic73—42no—
369Dic73—42no—
370Dic73—82no—
371Dic73C2×#9914yes—
372C2×#1996—731nomaximal, Sylow
373C2×C73—21no—
374C2×C73—21no—
375C2×C73—21no—
376C2×C73—21no—
377C2×C73—21no—
378C2×C73—21no—
379C2×C73—22no—
380C2×C73—22no—
381C2×C73—22no—
382C2×C73#199614yescomplemented
383C2×C73C2×#39111yescharacteristic
384C2×C73C22×#9911yescharacteristic
385C2×C73C2×#41011yescharacteristic
386C22×C22⋊Q8—731no—
387C2×#380—731no—
388C2×C4×C22⋊C4—731no—
389#1996—738no—
390C2×#342—731no—
391C2×#342—731no—
392C2×#342—731no—
393C2×#342D7311yescharacteristic
394C73C2×#199611yescharacteristic, complemented, Sylow
395C23×Q8—731no—
396C24×C4—731no—
397C2×C22⋊Q8—734no—
398C2×C22⋊Q8—734no—
399C2×C22⋊Q8—1461no—
400C2×C22⋊Q8—1461no—
401C2×C22⋊Q8—1462no—
402C2×C22⋊Q8—1462no—
403C2×C22⋊Q8—1461no—
404C2×C22⋊Q8—1461no—
405C22×C4⋊C4—731no—
406C22×C4⋊C4—731no—
407C22×C4⋊C4—731no—
408C22×C4⋊C4—1461no—
409C22×C22⋊C4—731no—
410C22×C22⋊C4—731no—
411C22×C22⋊C4—731no—
412C22×C22⋊C4C2×D7311yescharacteristic
413C22×C22⋊C4C2×D7311yescharacteristic
414C22×C22⋊C4C2×D7311yescharacteristic
415C22×C42—1461no—
416#380—734no—
417#380—1462no—
418C4×C22⋊C4—734no—
419C4×C22⋊C4—1462no—
420C2×#95—1461no—
421C2×#95—1461no—
422#342—734no—
423#342—734no—
424#342—734no—
425#342C2×D7314yes—
426C25C22×D7311yescharacteristic
427C22×Q8—2924no—
428C22×Q8—734no—
429C22×Q8—1462no—
430C22×Q8—1461no—
431C22×Q8—1461no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—2924no—
435C23×C4—731no—
436C23×C4—732no—
437C23×C4—731no—
438C23×C4—731no—
439C23×C4—732no—
440C23×C4—732no—
441C23×C4—732no—
442C23×C4—731no—
443C23×C4—731no—
444C23×C4—731no—
445C23×C4—731no—
446C23×C4—731no—
447C23×C4—1461no—
448C23×C4—1461no—
449C23×C4C4×D7311yescharacteristic
450C23×C4C4×D7311yescharacteristic
451C22⋊Q8—1464no—
452C22⋊Q8—1464no—
453C22⋊Q8—1464no—
454C22⋊Q8—1464no—
455C22⋊Q8—1464no—
456C22⋊Q8—1464no—
457C22⋊Q8—1464no—
458C22⋊Q8—1464no—
459C2×C4⋊C4—2924no—
460C2×C4⋊C4—734no—
461C2×C4⋊C4—734no—
462C2×C4⋊C4—734no—
463C2×C4⋊C4—1464no—
464C2×C4⋊C4—1462no—
465C2×C4⋊C4—1462no—
466C2×C4⋊C4—1461no—
467C2×C4⋊C4—1461no—
468C2×C4⋊C4—1461no—
469C2×C4⋊C4—1461no—
470C2×C4⋊C4—1462no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1461no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—734no—
483C2×C22⋊C4—732no—
484C2×C22⋊C4—732no—
485C2×C22⋊C4—732no—
486C2×C22⋊C4—732no—
487C2×C22⋊C4—1461no—
488C2×C22⋊C4—1462no—
489C2×C22⋊C4—1462no—
490C2×C22⋊C4—1461no—
491C2×C22⋊C4—1461no—
492C2×C22⋊C4—1461no—
493C2×C22⋊C4—1461no—
494C2×C22⋊C4—1461no—
495C2×C22⋊C4—1462no—
496C2×C22⋊C4Dic14614yescomplemented
497C2×C22⋊C4C4×D7312yes—
498C2×C22⋊C4C22×D7312yes—
499C2×C22⋊C4C22×D7312yes—
500C2×C22⋊C4C22×D7312yes—
501C2×C42—2924no—
502C2×C42—1464no—
503#95—1464no—
504#95—1464no—
505C24—42no—
506C24—42no—
507C24C2×C4×D7311yescharacteristic
508C24C2×C4×D7311yescharacteristic
509C24D4×D7311yescharacteristic
510C24D4×D7311yescharacteristic
511C24D4×D7311yescharacteristic
512C24D4×D7311yescharacteristic
513C24Q8×D7312yes—
514C24C2×Dic14612yes—
515C24#1192402712yes—
516C24#1192402812yes—
517C24C23×D7311yescharacteristic
518C2×Q8—2924no—
519C2×Q8—2928no—
520C2×Q8—2928no—
521C2×Q8—2924no—
522C2×Q8—1464no—
523C2×Q8—1464no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—2922no—
539C22×C4—2922no—
540C22×C4—2922no—
541C22×C4—2922no—
542C22×C4—2922no—
543C22×C4—2922no—
544C22×C4—2922no—
545C22×C4—2924no—
546C22×C4—2924no—
547C22×C4—2924no—
548C22×C4—2924no—
549C22×C4—2922no—
550C22×C4—2922no—
551C22×C4—2922no—
552C22×C4—732no—
553C22×C4—732no—
554C22×C4—732no—
555C22×C4—732no—
556C22×C4—732no—
557C22×C4—732no—
558C22×C4—732no—
559C22×C4—732no—
560C22×C4—731no—
561C22×C4—732no—
562C22×C4—732no—
563C22×C4—732no—
564C22×C4—731no—
565C22×C4—731no—
566C22×C4—731no—
567C22×C4—732no—
568C22×C4—732no—
569C22×C4—732no—
570C22×C4—1462no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1464no—
576C22×C4—1462no—
577C22×C4—1464no—
578C22×C4—1464no—
579C22×C4—1464no—
580C22×C4C2×C4×D7312yes—
581C22×C4C2×C4×D7312yes—
582C4⋊C4—2928no—
583C4⋊C4—1464no—
584C4⋊C4—1464no—
585C4⋊C4—1464no—
586C4⋊C4—1464no—
587C4⋊C4—1464no—
588C4⋊C4—1464no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—24no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—42no—
598C22⋊C4—2922no—
599C22⋊C4—734no—
600C22⋊C4—1462no—
601C22⋊C4—1462no—
602C22⋊C4—1462no—
603C22⋊C4—1462no—
604C22⋊C4—1464no—
605C22⋊C4—1462no—
606C22⋊C4—1462no—
607C22⋊C4—1462no—
608C22⋊C4C2×Dic14614yescomplemented
609C42—2928no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—41no—
628C23C22⋊C4×D7311yescharacteristic
629C23C22⋊C4×D7311yescharacteristic
630C23C22⋊C4×D7311yescharacteristic
631C23C22⋊C4×D7311yescharacteristic
632C23#1455655612yes—
633C23#1455655612yes—
634C23C4×Dic14612yes—
635C23C4×Dic14612yes—
636C23#1455656812yes—
637C23#1455656812yes—
638C23#1455656912yes—
639C23#1455656912yes—
640C23#1455657712yes—
641C23#1455657712yes—
642C23#1455659012yes—
643C23#1455659012yes—
644C23C22×C4×D7311yescharacteristic
645C23C2×D4×D7311yescharacteristic
646C23C2×D4×D7311yescharacteristic
647C23C2×Q8×D7311yescharacteristic
648C23C22×Dic14611yescharacteristic
649C23C2×#1192402711yescharacteristic
650C23C2×#1192402811yescharacteristic
651Q8—2928no—
652Q8—2928no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—48no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—2922no—
670C2×C4—2922no—
671C2×C4—2922no—
672C2×C4—2928no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—2922no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—2922no—
680C2×C4—2922no—
681C2×C4—2922no—
682C2×C4—2922no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—2922no—
686C2×C4—2922no—
687C2×C4—5844no—
688C2×C4—732no—
689C2×C4—734no—
690C2×C4—732no—
691C2×C4—732no—
692C2×C4—732no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1464no—
696C2×C4—1464no—
697C2×C4—1464no—
698C2×C4—1464no—
699C2×C4—1464no—
700C2×C4—1464no—
701C2×C4—1464no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—24no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22#1798849112yes—
734C22#1798849112yes—
735C22#1798849112yes—
736C22#1798849112yes—
737C22#99×D7312yes—
738C22#1798855912yes—
739C22C2×C22⋊C4×D7311yescharacteristic
740C22C2×#1455655611yescharacteristic
741C22C2×C4×Dic14611yescharacteristic
742C22C2×#1455656811yescharacteristic
743C22C2×#1455656911yescharacteristic
744C22C2×#1455657711yescharacteristic
745C22C2×#1455659011yescharacteristic
746C4—44no—
747C4—42no—
748C4—42no—
749C4—82no—
750C4—2924no—
751C4—2922no—
752C4—2922no—
753C4—5842no—
754C4—734no—
755C4—1462no—
756C4—1462no—
757C4—1462no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—22no—
763C2—22no—
764C2—22no—
765C2—21no—
766C2—21no—
767C2#2261091414yesdirect product factor
768C2C2×#1798849111yescharacteristic
769C2C2×#99×D7311yescharacteristic
770C2C2×#1798855911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC2×#342×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC25×C73C23
cosocleC24×C73C24
hypercenterC2×#342D73
hypocenterC73C2×#1996
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #22610914C2direct (N × H)
9. C23×Dic146C4semidirect
17. C2×#14556568C4semidirect
19. C22×C4⋊Dic73C4semidirect
21. C22×#11924007C4semidirect
22. C22×#11924007C4semidirect
44. C22×Dic146C2×C4semidirect
71. C2×C4⋊Dic73C2×C4semidirect
80. C2×#11924007C2×C4semidirect
81. C2×#11924007C2×C4semidirect
92. C2×C22⋊Dic73Q8semidirect
115. C2×C22⋊C4×C73Q8semidirect
183. C22⋊Dic73C2×Q8semidirect
223. C22⋊C4×C73C2×Q8semidirect
382. C2×C73#1996semidirect
394. C73C2×#1996semidirect
496. C2×C22⋊C4Dic146semidirect
608. C22⋊C4C2×Dic146semidirect
767. C2#22610914direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565682
C2×#179884452
C2×C22⋊C4×Dic732
#226109142
C2×#179883542
C2×#179883532
C2×#342×C732
C2×#199673