Finite Group Databasebeta

← C2×#22619779 #33953562

Subgroups — C2×#22619779 #33953562

Order 18688.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989214C211yesmaximal, characteristic, complemented
2C2×#17989069C211yesmaximal, characteristic
3#22619779C2116yesmaximal, direct product factor
4C2×#17988894C211yesmaximal, characteristic, complemented
5C2×#17988892C211yesmaximal, characteristic, complemented
6C2×#17988880C211yesmaximal, characteristic, complemented
7C2×#17988890C211yesmaximal, characteristic, complemented
8C2×#17988888C211yesmaximal, characteristic, complemented
9C2×#17988866C211yesmaximal, characteristic, complemented
10C2×#17988864C211yesmaximal, characteristic, complemented
11C2×#17988628C211yesmaximal, characteristic, complemented
12C2×#107×D73C211yesmaximal, characteristic, complemented
13C2×#17988612C211yesmaximal, characteristic, complemented
14C2×#17988587C211yesmaximal, characteristic
15C2×#17988582C211yesmaximal, characteristic
16C2×#477×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20#17989214—24no—
21#17989214C2218yescomplemented
22C2×#14556590C2211yescharacteristic
23C2×#14556589—21no—
24C2×#14556583C2211yescharacteristic
25C2×#14556582C2211yescharacteristic
26C2×#14556581—21no—
27C2×#14556569—21no—
28C2×#14556567—21no—
29#17989069—24no—
30#17989069C2218yes—
31C2×Q8×Dic73C2211yescharacteristic
32C2×C4×D292—21no—
33C2×C4×D292C2211yescharacteristic
34C2×#14556553—21no—
35C2×#14556553C2211yescharacteristic
36C2×#14556549C2211yescharacteristic
37C2×#14556548—21no—
38C2×#14556548C2211yescharacteristic
39C2×C4⋊C4×D73—21no—
40C2×C4⋊C4×D73C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42#17988894C2218yescomplemented
43#17988892C2218yescomplemented
44#17988890C2218yescomplemented
45#17988888C2218yescomplemented
46#17988880C2218yescomplemented
47#17988866C2218yescomplemented
48#17988864C2218yescomplemented
49#17988628C2218yescomplemented
50C2×#14556525C2211yescharacteristic
51C2×#14556524C2211yescharacteristic
52C2×#14556524C2211yescharacteristic
53C2×#14556524C2211yescharacteristic
54#107×D73C2218yescomplemented
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57#17988612C2218yescomplemented
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61#17988587C2218yes—
62#17988582C2218yes—
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556511C2211yescharacteristic
68C2×#14556511C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71#477×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#107×C73C2211yescharacteristic
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029Q818yescomplemented
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×C4×D73—21no—
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73C2311yescharacteristic
90C2×#11924011—24no—
91C2×#11924011C2314yes—
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94C2×C8×D73—24no—
95C2×C8×D73C2314yes—
96#14556590—22no—
97#14556590C2314yes—
98#14556589—28no—
99#14556583—22no—
100#14556583C2314yes—
101#14556582—22no—
102#14556582C2314yes—
103#14556581—28no—
104#14556569—28no—
105#14556567—28no—
106Q8×Dic73—22no—
107Q8×Dic73C2314yes—
108C4×D292—28no—
109C4×D292—22no—
110C4×D292C2314yes—
111#14556553—28no—
112#14556553—22no—
113#14556553C2314yes—
114#14556549—22no—
115#14556549C2314yes—
116#14556548—28no—
117#14556548D414yes—
118#14556548C2314yes—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007D411yescharacteristic
131C2×#11924007D411yescharacteristic
132C4⋊C4×D73—22no—
133C4⋊C4×D73—22no—
134C4⋊C4×D73—28no—
135C4⋊C4×D73C2314yes—
136C4⋊C4×D73C2314yes—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005D411yescharacteristic
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yes—
146#14556524C2314yes—
147#14556524C2314yes—
148#14556524C2314yes—
149#14556523C2314yes—
150#14556522C2314yes—
151C4⋊#10596831C2314yes—
152#14556520C2314yes—
153#14556520C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556513C2314yes—
157#14556513C2314yes—
158#14556511C2314yes—
159#14556511C2314yes—
160C22×Q8×C73—21no—
161C22×Q8×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C4⋊Q8×C73—22no—
165C4⋊Q8×C73C2314yes—
166C4×Q8×C73—22no—
167C4×Q8×C73C2314yes—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C42×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#107×C73C2314yes—
176#107×C73C2314yes—
177C4⋊C8×C73C2314yes—
178#103×C73C2314yes—
179#103×C73C2314yes—
180C23×D73—21no—
181C23×D73C2×D411yescharacteristic
182#11924029—216no—
183#11924029—28no—
184#11924029C2×Q8116yescomplemented
185C2×Dic146—24no—
186C2×Dic146—82no—
187C2×D292—28no—
188C2×D292—24no—
189C2×D292—21no—
190C2×D292—22no—
191C2×D292C2×Q814yes—
192C2×D292C2412yes—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73C2×D411yescharacteristic
197C22×Dic73C2×D411yescharacteristic
198C22×Dic73C2×D411yescharacteristic
199C2×C4×D73—28no—
200C2×C4×D73—24no—
201C2×C4×D73—24no—
202C2×C4×D73—24no—
203C2×C4×D73—24no—
204C2×C4×D73—24no—
205C2×C4×D73—82no—
206C2×C4×D73—82no—
207C2×C4×D73—82no—
208C2×C4×D73—82no—
209C2×C4×D73C2×D412yes—
210C2×C4×D73C2×Q814yes—
211C2×C4×D73#4114yes—
212C2×C4×D73C2412yes—
213#11924011—28no—
214C2×#10596831—22no—
215C2×#10596831—22no—
216C2×#10596831C2412yes—
217C2×#10596831C2412yes—
218C8×D73—28no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—24no—
223C4⋊Dic73—24no—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226C4⋊Dic73C2412yes—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007C2×D414yes—
234#11924007C2×D414yes—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005C2×D414yes—
239#11924005C2×D414yes—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C4×Dic73C2×D412yes—
243C4×Dic73C2412yes—
244C2×Q8×C73—21no—
245C2×Q8×C73—24no—
246C2×Q8×C73—22no—
247C2×Q8×C73—82no—
248C2×Q8×C73C2×Q814yes—
249C2×Q8×C73C2412yes—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2411yescharacteristic
257C2×C8×C73—22no—
258C2×C8×C73—22no—
259C2×C8×C73C2412yes—
260C2×C8×C73C2412yes—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C42×C73—24no—
270C42×C73C2×D412yes—
271C42×C73C2412yes—
272C23×C73C22×D411yescharacteristic
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—24no—
276C22×D73—22no—
277C22×D73—42no—
278C22×D73—42no—
279C22×D73C22⋊Q814yes—
280C22×D73C22×D412yes—
281Q8×C73—24no—
282Q8×C73—22no—
283Q8×C73—84no—
284Q8×C73C22×Q814yes—
285C2×C4×C73—24no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D412yes—
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C22×Q812yes—
299C2×C4×C73C2×#4112yes—
300C2×C4×C73C2511yescharacteristic
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—42no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73C22⋊Q814yes—
310C2×Dic73C22×D412yes—
311C2×Dic73C22×D412yes—
312C2×Dic73C22×D412yes—
313D292—216no—
314D292—24no—
315D292—22no—
316D292C22×Q814yes—
317C4×D73—216no—
318C4×D73—84no—
319C4×D73—84no—
320C4×D73—84no—
321C4×D73—84no—
322C4×D73C22⋊Q818yes—
323C4×D73C22×Q814yes—
324C4×D73C2×#4114yes—
325Dic146—84no—
326C8×C73—22no—
327C8×C73—22no—
328#10596831—22no—
329#10596831—22no—
330C22×C73C2×C22⋊Q812yes—
331C22×C73#57612yes—
332C22×C73#57812yes—
333C22×C73C23×D411yescharacteristic
334C2×D73—28no—
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—24no—
338C2×D73—48no—
339C2×D73—42no—
340C2×D73—42no—
341C2×D73C2×C22⋊Q814yes—
342C4×C73—24no—
343C4×C73—22no—
344C4×C73—22no—
345C4×C73—42no—
346C4×C73—42no—
347C4×C73—42no—
348C4×C73C2×C22⋊Q812yes—
349C4×C73C23×Q811yescharacteristic
350C4×C73C22×#4111yescharacteristic
351Dic73—22no—
352Dic73—22no—
353Dic73—42no—
354Dic73—42no—
355Dic73—42no—
356Dic73C2×C22⋊Q814yes—
357C2×#3083—731nomaximal, Sylow
358C2×C73#308314yescomplemented
359C2×C73C22×C22⋊Q811yescharacteristic
360C2×C73C2×#57611yescharacteristic
361C2×C73C2×#57811yescharacteristic
362D73—24no—
363D73—44no—
364C2×#544—731no—
365C2×#520—731no—
366#3083—7316no—
367C2×#479—731no—
368C2×#479—731no—
369C2×#477—731no—
370C2×#477D7311yescharacteristic, complemented
371C2×#478—731no—
372C2×#478—731no—
373C2×#474—731no—
374C2×#474—731no—
375C2×#428—731no—
376C22×#107—731no—
377C2×#424—731no—
378C2×#417—731no—
379C2×#416—731no—
380C73C2×#308311yescharacteristic, complemented, Sylow
381C22×#41—731no—
382C22×M16—731no—
383C23×C8—731no—
384#544—738no—
385#544—1464no—
386C2×C4⋊Q8—731no—
387C2×C4⋊Q8—1461no—
388C2×C4⋊Q8C2×D7311yescharacteristic
389C2×#125—731no—
390C2×#125—731no—
391C2×#125—1461no—
392C2×C22⋊Q8—1461no—
393C2×C22⋊Q8—1461no—
394#520—738no—
395#520—1464no—
396C2×C4×Q8—731no—
397C2×C4×Q8C2×D7311yescharacteristic
398C2×C4×D4—731no—
399C2×C4×D4—731no—
400C2×C4×D4—1461no—
401C2×C4×D4—1461no—
402C2×#117—731no—
403C2×#117—731no—
404C2×#117—1461no—
405C22×C4⋊C4—731no—
406C22×C4⋊C4—731no—
407C22×C4⋊C4—1461no—
408#479—738no—
409#479—738no—
410#478—738no—
411#478—738no—
412#477—738no—
413#477C2×D7318yescomplemented
414#474—738no—
415#474—738no—
416#428—738no—
417C2×#107—731no—
418C2×#107—731no—
419C2×#107—731no—
420C2×#107—731no—
421C2×#107—738no—
422C2×#107C2×D7311yescharacteristic
423C2×#107C2×D7311yescharacteristic
424C2×#106—731no—
425C2×#106—731no—
426#424—738no—
427C2×C4⋊C8—731no—
428C2×C4⋊C8—731no—
429C2×C4⋊C8—731no—
430C2×C4⋊C8C2×D7311yescharacteristic
431#417—738no—
432#416—738no—
433C2×#103—731no—
434C2×#103—731no—
435C2×#103C2×D7311yescharacteristic
436C2×#103C2×D7311yescharacteristic
437C2×#102—731no—
438C2×#102—731no—
439C2×#102—731no—
440C2×#102—731no—
441C2×#41—738no—
442C2×#41—734no—
443C2×#41—1462no—
444C2×#41—1464no—
445C22×Q8—21no—
446C22×Q8—1461no—
447C22×Q8C22×D7311yescharacteristic
448C22×D4—731no—
449C22×D4—1461no—
450C23×C4—731no—
451C23×C4—1461no—
452C23×C4—1461no—
453C23×C4—1461no—
454C23×C4—1461no—
455C23×C4—1461no—
456C2×M16—734no—
457C2×M16—1464no—
458C22×C8—731no—
459C22×C8—731no—
460C22×C8—734no—
461C22×C8—1464no—
462C22×C8C22×D7311yescharacteristic
463C22×C8C22×D7311yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8—734no—
466C4⋊Q8—1462no—
467C4⋊Q8—1468no—
468C4⋊Q8C22×D7314yes—
469#125—734no—
470#125—734no—
471#125—1462no—
472#125—1468no—
473#125—1462no—
474C22⋊Q8—1468no—
475C22⋊Q8—1468no—
476C4×Q8—22no—
477C4×Q8—734no—
478C4×Q8—1462no—
479C4×Q8C22×D7314yes—
480C4×D4—734no—
481C4×D4—734no—
482C4×D4—1468no—
483C4×D4—1462no—
484C4×D4—1468no—
485C4×D4—1462no—
486#117—734no—
487#117—734no—
488#117—734no—
489#117—1468no—
490#117—1462no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—731no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—734no—
499C2×C4⋊C4—734no—
500C2×C4⋊C4—1468no—
501C2×C4⋊C4—1462no—
502C2×C4⋊C4—1462no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4C22×D7311yescharacteristic
512C2×C4⋊C4C22×D7311yescharacteristic
513C2×C4⋊C4C22×D7311yescharacteristic
514C2×C22⋊C4—731no—
515C2×C22⋊C4—731no—
516C2×C22⋊C4—1461no—
517C2×C22⋊C4—1461no—
518C2×C22⋊C4—1461no—
519C2×C42—21no—
520C2×C42—731no—
521C2×C42—1461no—
522C2×C42—1461no—
523C2×C42C22×D7311yescharacteristic
524#107—734no—
525#107—734no—
526#107—734no—
527#107—734no—
528#107C22×D7314yes—
529#107C22×D7314yes—
530#106—734no—
531#106—734no—
532C4⋊C8—734no—
533C4⋊C8—734no—
534C4⋊C8—734no—
535C4⋊C8C22×D7314yes—
536#103—734no—
537#103—734no—
538#103C22×D7314yes—
539#103C22×D7314yes—
540#102—734no—
541#102—734no—
542#102—734no—
543#102—734no—
544C24—731no—
545C24—1461no—
546#41—7316no—
547#41—1468no—
548#41—14616no—
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—82no—
553C2×Q8—5842no—
554C2×Q8—1464no—
555C2×Q8Q8×D7314yes—
556C2×Q8C23×D7312yes—
557C2×D4—734no—
558C2×D4—732no—
559C2×D4—1464no—
560C2×D4—1468no—
561C2×D4—1461no—
562C2×D4—1462no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—5842no—
568C22×C4—5842no—
569C22×C4—5842no—
570C22×C4—5842no—
571C22×C4—731no—
572C22×C4—732no—
573C22×C4—734no—
574C22×C4—734no—
575C22×C4—732no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—1464no—
579C22×C4—1464no—
580C22×C4—1464no—
581C22×C4—1464no—
582C22×C4—1468no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1464no—
587C22×C4D4×D7311yescharacteristic
588C22×C4D4×D7311yescharacteristic
589C22×C4C23×D7311yescharacteristic
590M16—1468no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—732no—
594C2×C8—732no—
595C2×C8—1468no—
596C2×C8—1462no—
597C2×C8—1462no—
598C2×C8C23×D7312yes—
599C2×C8C23×D7312yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—734no—
606C4⋊C4—734no—
607C4⋊C4—732no—
608C4⋊C4—732no—
609C4⋊C4—732no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1464no—
617C4⋊C4—1464no—
618C4⋊C4—1461no—
619C4⋊C4—1461no—
620C4⋊C4—1461no—
621C4⋊C4C23×D7312yes—
622C4⋊C4C23×D7312yes—
623C4⋊C4C23×D7312yes—
624C22⋊C4—734no—
625C22⋊C4—734no—
626C22⋊C4—1464no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C42—24no—
630C42—732no—
631C42—732no—
632C42—1464no—
633C42—1464no—
634C42D4×D7312yes—
635C42C23×D7312yes—
636C23—2922no—
637C23—2922no—
638C23—732no—
639C23—734no—
640C23—1462no—
641C23—1464no—
642C23—1462no—
643C23—1462no—
644C23C2×D4×D7311yescharacteristic
645Q8—22no—
646Q8—24no—
647Q8—84no—
648Q8—5844no—
649Q8C2×Q8×D7314yes—
650D4—734no—
651D4—14616no—
652D4—1462no—
653D4—1464no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—2922no—
665C2×C4—2922no—
666C2×C4—2922no—
667C2×C4—5844no—
668C2×C4—5844no—
669C2×C4—5844no—
670C2×C4—5844no—
671C2×C4—732no—
672C2×C4—734no—
673C2×C4—734no—
674C2×C4—734no—
675C2×C4—738no—
676C2×C4—732no—
677C2×C4—732no—
678C2×C4—14616no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4C2×D4×D7312yes—
685C2×C4C2×D4×D7312yes—
686C2×C4C2×D4×D7311yescharacteristic
687C2×C4C2×Q8×D7312yes—
688C2×C4#41×D7312yes—
689C2×C4C24×D7311yescharacteristic
690C8—22no—
691C8—22no—
692C8—1462no—
693C8—1462no—
694C22—2928no—
695C22—2922no—
696C22—2922no—
697C22—734no—
698C22—1464no—
699C22—1468no—
700C22—1462no—
701C22—1462no—
702C22C22⋊Q8×D7312yes—
703C22#1798939112yes—
704C22#1798940012yes—
705C22C22×D4×D7311yescharacteristic
706C4—22no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—2922no—
713C4—2922no—
714C4—2922no—
715C4—734no—
716C4—1462no—
717C4—1462no—
718C4C22⋊Q8×D7312yes—
719C4C22×Q8×D7311yescharacteristic
720C4C2×#41×D7311yescharacteristic
721C2—2924no—
722C2—1464no—
723C2#2261977914yesdirect product factor
724C2C2×C22⋊Q8×D7311yescharacteristic
725C2C2×#1798939111yescharacteristic
726C2C2×#1798940011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#477×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924029C22
hypercenterC2×#477D73
hypocenterC73C2×#3083
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#17989214C2semidirect
3. #22619779C2direct (N × H)
4. C2×#17988894C2semidirect
5. C2×#17988892C2semidirect
6. C2×#17988880C2semidirect
7. C2×#17988890C2semidirect
8. C2×#17988888C2semidirect
9. C2×#17988866C2semidirect
10. C2×#17988864C2semidirect
11. C2×#17988628C2semidirect
12. C2×#107×D73C2semidirect
13. C2×#17988612C2semidirect
16. C2×#477×C73C2semidirect
21. #17989214C22semidirect
42. #17988894C22semidirect
43. #17988892C22semidirect
44. #17988890C22semidirect
45. #17988888C22semidirect
46. #17988880C22semidirect
47. #17988866C22semidirect
48. #17988864C22semidirect
49. #17988628C22semidirect
54. #107×D73C22semidirect
57. #17988612C22semidirect
71. #477×C73C22semidirect
79. C2×#11924029Q8semidirect
184. #11924029C2×Q8semidirect
358. C2×C73#3083semidirect
370. C2×#477D73semidirect
380. C73C2×#3083semidirect
413. #477C2×D73semidirect
723. C2#22619779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892142
C2×#179890692
#226197792
C2×#179888942
C2×#179888922
C2×#179888802
C2×#179888902
C2×#179888882
C2×#179888662
C2×#179888642
C2×#179886282
C2×#107×D732
C2×#179886122
C2×#179885872
C2×#179885822
C2×#477×C732
C2×#308373