Finite Group Databasebeta

← C2×#22619995 #33954050

Subgroups — C2×#22619995 #33954050

Order 18688.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989139C211yesmaximal, characteristic, complemented
2C2×#41×Dic73C211yesmaximal, characteristic
3#22619995C2116yesmaximal, direct product factor
4C2×#17988929C211yesmaximal, characteristic, complemented
5C2×#17988925C211yesmaximal, characteristic, complemented
6C2×#17988870C211yesmaximal, characteristic, complemented
7C2×#17988865C211yesmaximal, characteristic, complemented
8C2×#17988795C211yesmaximal, characteristic, complemented
9C2×#17988790C211yesmaximal, characteristic, complemented
10C2×#17988749C211yesmaximal, characteristic
11C2×Q16×Dic73C211yesmaximal, characteristic, complemented
12C2×#17988679C211yesmaximal, characteristic, complemented
13C2×#17988678C211yesmaximal, characteristic, complemented
14C2×SD16×Dic73C211yesmaximal, characteristic, complemented
15C2×#17988637C211yesmaximal, characteristic, complemented
16C2×#452×C73C211yesmaximal, characteristic
17C22×#11924018C2211yescharacteristic
18C22×#11924016C2211yescharacteristic
19#17989139—24no—
20#17989139C2218yescomplemented
21C2×#14556590C2211yescharacteristic
22C2×#14556589C2211yescharacteristic
23C2×#14556581—21no—
24C2×#14556570C2211yescharacteristic
25C2×#14556568—21no—
26#41×Dic73—24no—
27#41×Dic73C2218yes—
28C2×Q8×Dic73C2211yescharacteristic
29C2×Q8×Dic73C2211yescharacteristic
30C2×Q8×Dic73C2211yescharacteristic
31C2×#14556556—21no—
32C2×#14556556C2211yescharacteristic
33C2×D4×Dic73—21no—
34C2×D4×Dic73—21no—
35C2×D4×Dic73C2211yescharacteristic
36C2×D4×Dic73C2211yescharacteristic
37C2×#14556550—21no—
38C2×#14556550C2211yescharacteristic
39C2×#14556547—21no—
40C22×C4×Dic73—21no—
41C22×C4×Dic73C2211yescharacteristic
42#17988929C2218yescomplemented
43#17988925C2218yescomplemented
44#17988870C2218yescomplemented
45#17988865C2218yescomplemented
46#17988795C2218yescomplemented
47#17988790C2218yescomplemented
48#17988749C2218yes—
49Q16×Dic73C2218yescomplemented
50#17988679C2218yescomplemented
51#17988678C2218yescomplemented
52SD16×Dic73C2218yescomplemented
53#17988637C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×#41×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C22×SD16×C73C2211yescharacteristic
72C2×C22⋊Q8×C73C2211yescharacteristic
73#452×C73C2218yes—
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C23×Dic73—21no—
80C23×Dic73—21no—
81C23×Dic73D411yescharacteristic
82C23×Dic73D411yescharacteristic
83C2×#11924018—24no—
84C2×#11924018C2314yes—
85C2×#11924016—24no—
86C2×#11924016C2314yes—
87C22×#10596831C2311yescharacteristic
88C22×#10596831C2311yescharacteristic
89#14556590—22no—
90#14556590C2314yes—
91#14556589—22no—
92#14556589C2314yes—
93#14556581—28no—
94#14556570—22no—
95#14556570C2314yes—
96#14556568—28no—
97Q8×Dic73—22no—
98Q8×Dic73—22no—
99Q8×Dic73—22no—
100Q8×Dic73C2314yes—
101Q8×Dic73C2314yes—
102Q8×Dic73C2314yes—
103#14556556—22no—
104#14556556—28no—
105#14556556C2314yes—
106D4×Dic73—28no—
107D4×Dic73—28no—
108D4×Dic73—22no—
109D4×Dic73—22no—
110D4×Dic73C2314yes—
111D4×Dic73C2314yes—
112#14556550—28no—
113#14556550—22no—
114#14556550C2314yes—
115#14556547—28no—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73C2311yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×#11924007—21no—
123C2×#11924007—21no—
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×C22⋊Dic73—21no—
128C2×C22⋊Dic73—21no—
129C2×C22⋊Dic73—21no—
130C2×C22⋊Dic73—21no—
131C2×C4×Dic73—21no—
132C2×C4×Dic73—21no—
133C2×C4×Dic73—21no—
134C2×C4×Dic73—21no—
135C2×C4×Dic73—28no—
136C2×C4×Dic73—21no—
137C2×C4×Dic73D414yes—
138C2×C4×Dic73D411yescharacteristic
139C2×C4×Dic73D411yescharacteristic
140C2×C4×Dic73C2311yescharacteristic
141C2×C4×Dic73C2314yes—
142C2×C4×Dic73C2311yescharacteristic
143#14556525C2314yes—
144#14556524C2314yes—
145#14556523C2314yes—
146#14556522C2314yes—
147#14556520C2314yes—
148#14556520C2314yes—
149#14556516C2314yes—
150#14556516C2314yes—
151#14556515C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556512C2314yes—
155C22⋊#10596831C2314yes—
156C8×Dic73C2314yes—
157C8×Dic73C2314yes—
158C2×#41×C73—24no—
159C2×#41×C73—24no—
160C2×#41×C73—22no—
161C2×#41×C73C2314yes—
162C22×Q8×C73C2311yescharacteristic
163C22×Q8×C73C2311yescharacteristic
164C22×D4×C73—21no—
165C22×D4×C73C2311yescharacteristic
166C23×C4×C73—21no—
167C23×C4×C73C2311yescharacteristic
168C2×Q16×C73—24no—
169C2×Q16×C73C2314yes—
170C2×SD16×C73—24no—
171C2×SD16×C73C2314yes—
172C22×C8×C73C2311yescharacteristic
173C22×C8×C73C2311yescharacteristic
174C22⋊Q8×C73—22no—
175C22⋊Q8×C73C2314yes—
176C2×C4⋊C4×C73—21no—
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C22⋊C4×C73—21no—
179#103×C73C2314yes—
180#102×C73C2314yes—
181C22⋊C8×C73C2314yes—
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—21no—
185C2×Dic146—24no—
186C2×Dic146—44no—
187C2×Dic146C2412yes—
188C22×Dic73—24no—
189C22×Dic73—24no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—24no—
195C22×Dic73—24no—
196C22×Dic73—44no—
197C22×Dic73—44no—
198C22×Dic73C2×D411yescharacteristic
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D414yes—
201C22×Dic73C2×D414yes—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204#11924018—28no—
205#11924016—28no—
206C2×#10596831—22no—
207C2×#10596831—22no—
208C2×#10596831C2412yes—
209C2×#10596831C2412yes—
210C4⋊Dic73—21no—
211C4⋊Dic73—21no—
212C4⋊Dic73—21no—
213C4⋊Dic73—24no—
214C4⋊Dic73—24no—
215C4⋊Dic73—24no—
216C4⋊Dic73C2412yes—
217C4⋊Dic73C2412yes—
218C4⋊Dic73C2412yes—
219#11924007—24no—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224C22⋊Dic73—24no—
225C22⋊Dic73—24no—
226C22⋊Dic73—24no—
227C22⋊Dic73—24no—
228C4×Dic73—24no—
229C4×Dic73—24no—
230C4×Dic73—24no—
231C4×Dic73—24no—
232C4×Dic73—24no—
233C4×Dic73C2×D414yes—
234C4×Dic73C2×D414yes—
235C4×Dic73C2×D412yes—
236C4×Dic73C2×D412yes—
237C4×Dic73C2412yes—
238C4×Dic73C2412yes—
239C24×C73—21no—
240C24×C73C2×D411yescharacteristic
241#41×C73—216no—
242#41×C73—28no—
243#41×C73—28no—
244C2×Q8×C73—21no—
245C2×Q8×C73—21no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73—22no—
249C2×Q8×C73#4114yes—
250C2×Q8×C73C2412yes—
251C2×Q8×C73C2412yes—
252C2×D4×C73—28no—
253C2×D4×C73—24no—
254C2×D4×C73—21no—
255C2×D4×C73—22no—
256C2×D4×C73#4114yes—
257C2×D4×C73C2412yes—
258C22×C4×C73—28no—
259C22×C4×C73—21no—
260C22×C4×C73—24no—
261C22×C4×C73—22no—
262C22×C4×C73—22no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D412yes—
267C22×C4×C73C2412yes—
268C22×C4×C73C2411yescharacteristic
269Q16×C73—28no—
270SD16×C73—28no—
271C2×C8×C73—22no—
272C2×C8×C73—22no—
273C2×C8×C73C2412yes—
274C2×C8×C73C2412yes—
275C4⋊C4×C73—24no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73C2412yes—
278C22⋊C4×C73—24no—
279C23×C73—22no—
280C23×C73—24no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73C22×D412yes—
287C23×C73C22×D411yescharacteristic
288Q8×C73—24no—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—42no—
293Q8×C73C2×#4114yes—
294D4×C73—216no—
295D4×C73—24no—
296D4×C73—22no—
297D4×C73C2×#4114yes—
298C2×C4×C73—216no—
299C2×C4×C73—22no—
300C2×C4×C73—24no—
301C2×C4×C73—22no—
302C2×C4×C73—24no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—42no—
308C2×C4×C73—42no—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C22×D411yescharacteristic
311C2×C4×C73C2×#4112yes—
312C2×C4×C73C2×#4112yes—
313C2×C4×C73C2511yescharacteristic
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—28no—
317C2×Dic73—28no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—48no—
327C2×Dic73—48no—
328C2×Dic73#13514yes—
329C2×Dic73#13714yes—
330C2×Dic73C22×D412yes—
331C2×Dic73C22×D412yes—
332C2×Dic73C22×D412yes—
333C2×Dic73C22×D412yes—
334Dic146—22no—
335Dic146—22no—
336Dic146—42no—
337Dic146—48no—
338C8×C73—22no—
339C8×C73—22no—
340#10596831—22no—
341#10596831—22no—
342C22×C73—22no—
343C22×C73—24no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—44no—
347C22×C73—48no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73#52512yes—
351C22×C73C2×#13512yes—
352C22×C73C2×#13712yes—
353C22×C73C23×D411yescharacteristic
354C4×C73—22no—
355C4×C73—24no—
356C4×C73—42no—
357C4×C73—42no—
358C4×C73#52512yes—
359C4×C73C22×#4111yescharacteristic
360C4×C73C22×#4111yescharacteristic
361Dic73—22no—
362Dic73—22no—
363Dic73—42no—
364Dic73—42no—
365Dic73—42no—
366Dic73—42no—
367Dic73C2×#13514yes—
368Dic73C2×#13714yes—
369C2×#3107—731nomaximal, Sylow
370C2×C73—42no—
371C2×C73—44no—
372C2×C73#310714yescomplemented
373C2×C73C2×#52511yescharacteristic
374C2×C73C22×#13511yescharacteristic
375C2×C73C22×#13711yescharacteristic
376C2×#533—731no—
377C2×C4×#41—731no—
378#3107—7316no—
379C2×#485—731no—
380C2×#485—731no—
381C2×#475—731no—
382C2×#474—731no—
383C2×#462—731no—
384C2×#461—731no—
385C2×#452—731no—
386C2×#452D7311yescharacteristic
387C2×C4×Q16—731no—
388C2×C4×Q16—731no—
389C2×C4×SD16—731no—
390C2×C4×SD16—731no—
391C2×#431—731no—
392C73C2×#310711yescharacteristic, complemented, Sylow
393C22×#41C2×D7311yescharacteristic
394C22×Q16—731no—
395C22×Q16C2×D7311yescharacteristic
396C22×SD16—731no—
397C22×SD16C2×D7311yescharacteristic
398#533—738no—
399#533—1464no—
400C2×C4⋊Q8—731no—
401C2×C4⋊Q8—731no—
402C2×#125—1461no—
403C2×C22⋊Q8—731no—
404C2×C22⋊Q8—1461no—
405C2×C22⋊Q8C2×D7311yescharacteristic
406C4×#41—738no—
407C4×#41—1464no—
408C2×C4×Q8—731no—
409C2×C4×Q8—731no—
410C2×C4×Q8—731no—
411C2×C4×Q8—731no—
412C2×C4×Q8—1461no—
413C2×C4×D4—731no—
414C2×C4×D4—731no—
415C2×C4×D4—1461no—
416C2×C4×D4—1461no—
417C2×#117—731no—
418C2×#117—1461no—
419C2×#117—1461no—
420C22×C42—731no—
421C22×C42—1461no—
422#485—738no—
423#485—738no—
424#475—738no—
425#474—738no—
426#462—738no—
427#461—738no—
428#452—738no—
429#452C2×D7318yes—
430C4×Q16—738no—
431C4×Q16—738no—
432C4×SD16—738no—
433C4×SD16—738no—
434#431—738no—
435C2×#107—731no—
436C2×#107—731no—
437C2×#106—731no—
438C2×#106—731no—
439C2×C4⋊C8—731no—
440C2×C4⋊C8—731no—
441C2×#103—731no—
442C2×#103—731no—
443C2×#103—731no—
444C2×#103—731no—
445C2×#103—731no—
446C2×#103C2×D7311yescharacteristic
447C2×#102—731no—
448C2×#102C2×D7311yescharacteristic
449C2×C22⋊C8—731no—
450C2×C22⋊C8C2×D7311yescharacteristic
451C2×C4×C8—731no—
452C2×C4×C8—731no—
453C2×#41—24no—
454C2×#41—24no—
455C2×#41—22no—
456C2×#41C22×D7314yes—
457C22×Q8—731no—
458C22×Q8—1461no—
459C22×Q8C22×D7311yescharacteristic
460C22×Q8C22×D7311yescharacteristic
461C22×D4—21no—
462C22×D4C22×D7311yescharacteristic
463C23×C4—21no—
464C23×C4—731no—
465C23×C4—731no—
466C23×C4—1461no—
467C23×C4—1461no—
468C23×C4C22×D7311yescharacteristic
469C2×Q16—24no—
470C2×Q16—734no—
471C2×Q16—1464no—
472C2×Q16C22×D7314yes—
473C2×SD16—24no—
474C2×SD16—734no—
475C2×SD16—1464no—
476C2×SD16C22×D7314yes—
477C22×C8—731no—
478C22×C8—731no—
479C22×C8C22×D7311yescharacteristic
480C22×C8C22×D7311yescharacteristic
481C4⋊Q8—734no—
482C4⋊Q8—734no—
483C4⋊Q8—1462no—
484C4⋊Q8—1462no—
485#125—1468no—
486C22⋊Q8—22no—
487C22⋊Q8—734no—
488C22⋊Q8—1468no—
489C22⋊Q8—1462no—
490C22⋊Q8C22×D7314yes—
491C4×Q8—734no—
492C4×Q8—734no—
493C4×Q8—734no—
494C4×Q8—734no—
495C4×Q8—1462no—
496C4×Q8—1468no—
497C4×Q8—1462no—
498C4×Q8—1462no—
499C4×Q8—1462no—
500C4×D4—734no—
501C4×D4—734no—
502C4×D4—1462no—
503C4×D4—1462no—
504C4×D4—1468no—
505C4×D4—1468no—
506#117—734no—
507#117—1468no—
508#117—1468no—
509#117—1462no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4C22×D7311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—731no—
529C2×C42—731no—
530C2×C42—734no—
531C2×C42—731no—
532C2×C42—731no—
533C2×C42—734no—
534C2×C42—1468no—
535C2×C42—1461no—
536C2×C42—1461no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42—1461no—
540#107—734no—
541#107—734no—
542#106—734no—
543#106—734no—
544C4⋊C8—734no—
545C4⋊C8—734no—
546#103—734no—
547#103—734no—
548#103—734no—
549#103—734no—
550#103—734no—
551#103C22×D7314yes—
552#102—734no—
553#102C22×D7314yes—
554C22⋊C8—734no—
555C22⋊C8C22×D7314yes—
556C4×C8—734no—
557C4×C8—734no—
558C24—21no—
559C24D4×D7311yescharacteristic
560#41—216no—
561#41—28no—
562#41—28no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—2924no—
569C2×Q8—732no—
570C2×Q8—1464no—
571C2×Q8—1462no—
572C2×Q8—1462no—
573C2×Q8—1461no—
574C2×Q8#1192402714yes—
575C2×Q8C23×D7312yes—
576C2×Q8C23×D7312yes—
577C2×D4—28no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4#1192402714yes—
582C2×D4C23×D7312yes—
583C22×C4—28no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—2924no—
591C22×C4—2924no—
592C22×C4—731no—
593C22×C4—731no—
594C22×C4—734no—
595C22×C4—734no—
596C22×C4—731no—
597C22×C4—731no—
598C22×C4—1464no—
599C22×C4—1464no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1464no—
605C22×C4—1464no—
606C22×C4D4×D7312yes—
607C22×C4D4×D7311yescharacteristic
608C22×C4C23×D7312yes—
609C22×C4C23×D7311yescharacteristic
610Q16—28no—
611Q16—1468no—
612SD16—28no—
613SD16—1468no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—732no—
617C2×C8—732no—
618C2×C8—1462no—
619C2×C8—1462no—
620C2×C8C23×D7312yes—
621C2×C8C23×D7312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—732no—
625C4⋊C4—732no—
626C4⋊C4—732no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1464no—
634C4⋊C4—1464no—
635C4⋊C4—1461no—
636C4⋊C4—1461no—
637C4⋊C4—1461no—
638C4⋊C4C23×D7312yes—
639C22⋊C4—24no—
640C22⋊C4—1464no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C42—734no—
645C42—734no—
646C42—732no—
647C42—732no—
648C42—732no—
649C42—732no—
650C42—1464no—
651C42—1464no—
652C42—1464no—
653C42—1464no—
654C42—1464no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23C2×D4×D7312yes—
663C23C2×D4×D7311yescharacteristic
664Q8—22no—
665Q8—24no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—2928no—
670Q8—2922no—
671Q8—1462no—
672Q8—1462no—
673Q8C2×#1192402714yes—
674D4—216no—
675D4—22no—
676D4—24no—
677D4C2×#1192402714yes—
678C2×C4—216no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—2922no—
690C2×C4—2922no—
691C2×C4—2922no—
692C2×C4—2922no—
693C2×C4—2928no—
694C2×C4—2928no—
695C2×C4—734no—
696C2×C4—732no—
697C2×C4—732no—
698C2×C4—734no—
699C2×C4—732no—
700C2×C4—732no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1468no—
706C2×C4—1468no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4C2×D4×D7312yes—
710C2×C4C2×D4×D7311yescharacteristic
711C2×C4C2×#1192402712yes—
712C2×C4C2×#1192402712yes—
713C2×C4C24×D7311yescharacteristic
714C8—22no—
715C8—22no—
716C8—1462no—
717C8—1462no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—24no—
722C22—44no—
723C22—48no—
724C22—42no—
725C22—42no—
726C22#1798909312yes—
727C22#135×D7312yes—
728C22#137×D7312yes—
729C22C22×D4×D7311yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—2922no—
735C4—2922no—
736C4—2922no—
737C4—2922no—
738C4—734no—
739C4—734no—
740C4—1462no—
741C4—1462no—
742C4#1798909312yes—
743C4C22×#1192402711yescharacteristic
744C4C22×#1192402711yescharacteristic
745C2—42no—
746C2—44no—
747C2#2261999514yesdirect product factor
748C2C2×#1798909311yescharacteristic
749C2C2×#135×D7311yescharacteristic
750C2C2×#137×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#452×C73C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
hypercenterC2×#452D73
hypocenterC73C2×#3107
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#17989139C2semidirect
3. #22619995C2direct (N × H)
4. C2×#17988929C2semidirect
5. C2×#17988925C2semidirect
6. C2×#17988870C2semidirect
7. C2×#17988865C2semidirect
8. C2×#17988795C2semidirect
9. C2×#17988790C2semidirect
11. C2×Q16×Dic73C2semidirect
12. C2×#17988679C2semidirect
13. C2×#17988678C2semidirect
14. C2×SD16×Dic73C2semidirect
15. C2×#17988637C2semidirect
20. #17989139C22semidirect
42. #17988929C22semidirect
43. #17988925C22semidirect
44. #17988870C22semidirect
45. #17988865C22semidirect
46. #17988795C22semidirect
47. #17988790C22semidirect
49. Q16×Dic73C22semidirect
50. #17988679C22semidirect
51. #17988678C22semidirect
52. SD16×Dic73C22semidirect
53. #17988637C22semidirect
372. C2×C73#3107semidirect
392. C73C2×#3107semidirect
747. C2#22619995direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891392
C2×#41×Dic732
#226199952
C2×#179889292
C2×#179889252
C2×#179888702
C2×#179888652
C2×#179887952
C2×#179887902
C2×#179887492
C2×Q16×Dic732
C2×#179886792
C2×#179886782
C2×SD16×Dic732
C2×#179886372
C2×#452×C732
C2×#310773