Finite Group Databasebeta

← C2×#22620059 #33954185

Subgroups — C2×#22620059 #33954185

Order 18688.

2118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989141C211yesmaximal, characteristic
2C2×C4×Q8×D73C211yesmaximal, characteristic
3#22620059C2116yesmaximal, direct product factor
4C2×#17988919C211yesmaximal, characteristic
5C2×#17988916C211yesmaximal, characteristic
6C2×#17988871C211yesmaximal, characteristic, complemented
7C2×#17988870C211yesmaximal, characteristic, complemented
8C2×#17988796C211yesmaximal, characteristic, complemented
9C2×#17988795C211yesmaximal, characteristic, complemented
10C2×#17988744C211yesmaximal, characteristic
11C2×#17988741C211yesmaximal, characteristic
12C2×#17988695C211yesmaximal, characteristic, complemented
13C2×#17988692C211yesmaximal, characteristic, complemented
14C2×#17988692C211yesmaximal, characteristic, complemented
15C2×#17988642C211yesmaximal, characteristic
16C2×#441×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21#17989141—24no—
22#17989141C2218yes—
23C2×#14556590C2211yescharacteristic
24C2×#14556589C2211yescharacteristic
25C2×#14556581—21no—
26C2×#14556571C2211yescharacteristic
27C2×#14556569—21no—
28C2×#14556567C2211yescharacteristic
29C2×Q8×Dic73C2211yescharacteristic
30C2×C4×Dic146—21no—
31C2×C4×Dic146—21no—
32C2×C4×Dic146C2211yescharacteristic
33C2×C4×Dic146C2211yescharacteristic
34C2×#14556556—21no—
35C2×#14556556C2211yescharacteristic
36C4×Q8×D73—24no—
37C4×Q8×D73C2218yes—
38C2×#14556548—21no—
39C2×C4⋊C4×D73—21no—
40C2×C4⋊C4×D73C2211yescharacteristic
41C2×C42×D73—21no—
42C2×C42×D73C2211yescharacteristic
43#17988919C2218yes—
44#17988916C2218yes—
45#17988871C2218yescomplemented
46#17988870C2218yescomplemented
47#17988796C2218yescomplemented
48#17988795C2218yescomplemented
49#17988744C2218yes—
50#17988741C2218yes—
51#17988695C2218yescomplemented
52#17988692C2218yescomplemented
53#17988692C2218yescomplemented
54#17988642C2218yes—
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556502C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×Q8×C73C2211yescharacteristic
72#441×C73C2218yescomplemented
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C22×Dic146C2311yescharacteristic
81C2×Q8×D73—24no—
82C2×Q8×D73—22no—
83C2×Q8×D73—24no—
84C2×Q8×D73C2314yes—
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73D411yescharacteristic
88C22×C4×D73D411yescharacteristic
89C22×C4×D73C2311yescharacteristic
90C2×Dic292—24no—
91C2×Dic292C2314yes—
92C2×#11924018—24no—
93C2×#11924018—24no—
94C2×#11924018C2314yes—
95C2×#11924018C2314yes—
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98#14556590—22no—
99#14556590C2314yes—
100#14556589—22no—
101#14556589C2314yes—
102#14556581—28no—
103#14556571—22no—
104#14556571C2314yes—
105#14556569—28no—
106#14556567—22no—
107#14556567C2314yes—
108Q8×Dic73—22no—
109Q8×Dic73C2314yes—
110C4×Dic146—28no—
111C4×Dic146—28no—
112C4×Dic146—22no—
113C4×Dic146—22no—
114C4×Dic146C2314yes—
115C4×Dic146C2314yes—
116#14556556—22no—
117#14556556—28no—
118#14556556C2314yes—
119#14556548—28no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73—21no—
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×#11924007—21no—
131C2×#11924007—21no—
132C4⋊C4×D73—28no—
133C4⋊C4×D73—22no—
134C4⋊C4×D73C2314yes—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×C4×Dic73—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73D411yescharacteristic
142C2×C4×Dic73D411yescharacteristic
143C2×C4×Dic73C2311yescharacteristic
144C42×D73—28no—
145C42×D73D414yes—
146C42×D73C2314yes—
147#14556523C2314yes—
148#14556522C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556514C2314yes—
157#14556514C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160#14556502C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C4×Q8×C73—22no—
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×Q8×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C42×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#106×C73C2314yes—
179#103×C73C2314yes—
180#103×C73C2314yes—
181#97×C73C2314yes—
182C23×D73C2×D411yescharacteristic
183C2×Dic146—28no—
184C2×Dic146—21no—
185C2×Dic146—22no—
186C2×Dic146—24no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146—24no—
191C2×Dic146—44no—
192C2×Dic146#4114yes—
193C2×Dic146C2412yes—
194C2×Dic146C2412yes—
195Q8×D73—216no—
196Q8×D73—28no—
197Q8×D73—28no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C2×C4×D73—28no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—22no—
209C2×C4×D73—22no—
210C2×C4×D73—24no—
211C2×C4×D73—24no—
212C2×C4×D73—44no—
213C2×C4×D73C2×D414yes—
214C2×C4×D73C2×D412yes—
215C2×C4×D73C2×D414yes—
216C2×C4×D73C2412yes—
217Dic292—28no—
218#11924018—28no—
219#11924018—28no—
220C2×#10596831—22no—
221C2×#10596831—22no—
222C2×#10596831C2412yes—
223C2×#10596831C2412yes—
224C4⋊Dic73—21no—
225C4⋊Dic73—21no—
226C4⋊Dic73—24no—
227C4⋊Dic73—24no—
228C4⋊Dic73C2412yes—
229C4⋊Dic73C2412yes—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924007—24no—
238#11924005—24no—
239#11924005—24no—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73C2×D412yes—
245C4×Dic73C2×D414yes—
246C4×Dic73C2×D414yes—
247C4×Dic73C2412yes—
248C2×Q8×C73—21no—
249C2×Q8×C73—21no—
250C2×Q8×C73—22no—
251C2×Q8×C73—22no—
252C2×Q8×C73—22no—
253C2×Q8×C73#4114yes—
254C2×Q8×C73C2412yes—
255C2×Q8×C73C2412yes—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2411yescharacteristic
263Q16×C73—28no—
264C2×C8×C73—22no—
265C2×C8×C73—22no—
266C2×C8×C73C2412yes—
267C2×C8×C73C2412yes—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—24no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73C2412yes—
273C4⋊C4×C73C2412yes—
274C42×C73—24no—
275C42×C73—24no—
276C42×C73C2×D412yes—
277C42×C73C2412yes—
278C23×C73C22×D411yescharacteristic
279C22×D73—22no—
280C22×D73—22no—
281C22×D73#13714yes—
282C22×D73C22×D412yes—
283Q8×C73—24no—
284Q8×C73—22no—
285Q8×C73—22no—
286Q8×C73—22no—
287Q8×C73—42no—
288Q8×C73C2×#4114yes—
289C2×C4×C73—24no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73—42no—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D412yes—
301C2×C4×C73C22×D411yescharacteristic
302C2×C4×C73C2×#4112yes—
303C2×C4×C73C2×#4112yes—
304C2×C4×C73C2511yescharacteristic
305C2×Dic73—24no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73#13714yes—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319C4×D73—216no—
320C4×D73—28no—
321C4×D73—24no—
322C4×D73—22no—
323C4×D73—22no—
324C4×D73—28no—
325C4×D73—48no—
326Dic146—216no—
327Dic146—24no—
328Dic146—22no—
329Dic146—22no—
330Dic146—22no—
331Dic146—42no—
332Dic146—48no—
333Dic146C2×#4114yes—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831—22no—
338C22×C73#52512yes—
339C22×C73C2×#13712yes—
340C22×C73C2×#13712yes—
341C22×C73C23×D411yescharacteristic
342C2×D73—28no—
343C2×D73—22no—
344C2×D73—22no—
345C2×D73C2×#13714yes—
346C4×C73—24no—
347C4×C73—22no—
348C4×C73—22no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73—42no—
352C4×C73#52512yes—
353C4×C73C22×#4111yescharacteristic
354C4×C73C22×#4111yescharacteristic
355Dic73—22no—
356Dic73—24no—
357Dic73—22no—
358Dic73—42no—
359Dic73—42no—
360Dic73—42no—
361Dic73C2×#13714yes—
362C2×#3113—731nomaximal, Sylow
363C2×C73#311314yescomplemented
364C2×C73C2×#52511yescharacteristic
365C2×C73C22×#13711yescharacteristic
366C2×C73C22×#13711yescharacteristic
367D73—24no—
368C2×#533—731no—
369C22×C4×Q8—731no—
370#3113—7316no—
371C2×#483—731no—
372C2×#483—731no—
373C2×#475—731no—
374C2×#475—731no—
375C2×#462—731no—
376C2×#462—731no—
377C2×#451—731no—
378C2×#451—731no—
379C2×#441—731no—
380C2×#441—731no—
381C2×#441—731no—
382C2×#441D7311yescharacteristic, complemented
383C2×#432—731no—
384C73C2×#311311yescharacteristic, complemented, Sylow
385C23×Q8—731no—
386C22×Q16—731no—
387C22×Q16—731no—
388C22×Q16—731no—
389C22×Q16C2×D7311yescharacteristic
390#533—738no—
391#533—1464no—
392C2×C4⋊Q8—731no—
393C2×C4⋊Q8—731no—
394C2×#125—1461no—
395C2×C22⋊Q8—731no—
396C2×C22⋊Q8—731no—
397C2×C22⋊Q8—1461no—
398C2×C4×Q8—731no—
399C2×C4×Q8—738no—
400C2×C4×Q8—731no—
401C2×C4×Q8—731no—
402C2×C4×Q8—731no—
403C2×C4×Q8—1461no—
404C2×C4×Q8—1461no—
405C2×C4×Q8—1461no—
406C2×C4×Q8—1464no—
407C2×C4×Q8C2×D7311yescharacteristic
408C2×C4×Q8C2×D7311yescharacteristic
409C2×#117—1461no—
410C22×C4⋊C4—731no—
411C22×C4⋊C4—1461no—
412C22×C42—731no—
413C22×C42—1461no—
414#483—738no—
415#483—738no—
416#475—738no—
417#475—738no—
418#462—738no—
419#462—738no—
420#451—738no—
421#451—738no—
422#441—738no—
423#441—738no—
424#441—738no—
425#441C2×D7318yescomplemented
426#432—738no—
427C2×#106—731no—
428C2×#106—731no—
429C2×#106—731no—
430C2×#106C2×D7311yescharacteristic
431C2×C4⋊C8—731no—
432C2×C4⋊C8—731no—
433C2×#103—731no—
434C2×#103—731no—
435C2×#103—731no—
436C2×#103—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103C2×D7311yescharacteristic
440C2×#103C2×D7311yescharacteristic
441C2×C22⋊C8—731no—
442C2×C22⋊C8—731no—
443C2×#97—731no—
444C2×#97C2×D7311yescharacteristic
445C22×Q8—734no—
446C22×Q8—731no—
447C22×Q8—731no—
448C22×Q8—1461no—
449C22×Q8—1461no—
450C22×Q8—1462no—
451C22×Q8—1464no—
452C22×Q8—1464no—
453C22×Q8C22×D7311yescharacteristic
454C22×Q8C22×D7311yescharacteristic
455C23×C4—731no—
456C23×C4—731no—
457C23×C4—731no—
458C23×C4—1461no—
459C23×C4—1461no—
460C2×Q16—24no—
461C2×Q16—734no—
462C2×Q16—734no—
463C2×Q16—734no—
464C2×Q16—1464no—
465C2×Q16—1464no—
466C2×Q16—1464no—
467C2×Q16C22×D7314yes—
468C22×C8—731no—
469C22×C8—731no—
470C22×C8C22×D7311yescharacteristic
471C22×C8C22×D7311yescharacteristic
472C4⋊Q8—734no—
473C4⋊Q8—734no—
474C4⋊Q8—1462no—
475C4⋊Q8—1462no—
476#125—1468no—
477C22⋊Q8—734no—
478C22⋊Q8—734no—
479C22⋊Q8—1462no—
480C22⋊Q8—1468no—
481C22⋊Q8—1462no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—734no—
485C4×Q8—734no—
486C4×Q8—734no—
487C4×Q8—734no—
488C4×Q8—1468no—
489C4×Q8—1468no—
490C4×Q8—1468no—
491C4×Q8—1462no—
492C4×Q8—1462no—
493C4×Q8—1462no—
494C4×Q8—1462no—
495C4×Q8C22×D7314yes—
496C4×Q8C22×D7314yes—
497#117—1468no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—734no—
503C2×C4⋊C4—1462no—
504C2×C4⋊C4—1468no—
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⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4C22×D7311yescharacteristic
516C2×C4⋊C4C22×D7311yescharacteristic
517C2×C22⋊C4—1461no—
518C2×C22⋊C4—1461no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—731no—
522C2×C42—731no—
523C2×C42—731no—
524C2×C42—734no—
525C2×C42—734no—
526C2×C42—1468no—
527C2×C42—1461no—
528C2×C42—1461no—
529C2×C42—1461no—
530C2×C42—1461no—
531C2×C42C22×D7311yescharacteristic
532#106—734no—
533#106—734no—
534#106—734no—
535#106C22×D7314yes—
536C4⋊C8—734no—
537C4⋊C8—734no—
538#103—734no—
539#103—734no—
540#103—734no—
541#103—734no—
542#103—734no—
543#103—734no—
544#103C22×D7314yes—
545#103C22×D7314yes—
546C22⋊C8—734no—
547C22⋊C8—734no—
548#97—734no—
549#97C22×D7314yes—
550C24—731no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—2924no—
557C2×Q8—734no—
558C2×Q8—732no—
559C2×Q8—732no—
560C2×Q8—1464no—
561C2×Q8—1464no—
562C2×Q8—1468no—
563C2×Q8—1462no—
564C2×Q8—1462no—
565C2×Q8—1468no—
566C2×Q8—14616no—
567C2×Q8—1468no—
568C2×Q8—1461no—
569C2×Q8—1461no—
570C2×Q8—1462no—
571C2×Q8#1192402814yes—
572C2×Q8C23×D7312yes—
573C2×Q8C23×D7312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—2924no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—734no—
583C22×C4—734no—
584C22×C4—732no—
585C22×C4—732no—
586C22×C4—1464no—
587C22×C4—1464no—
588C22×C4—1464no—
589C22×C4—1464no—
590C22×C4—1468no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1462no—
596C22×C4—1462no—
597C22×C4D4×D7311yescharacteristic
598C22×C4D4×D7311yescharacteristic
599C22×C4C23×D7311yescharacteristic
600Q16—28no—
601Q16—1468no—
602Q16—1468no—
603Q16—1468no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—732no—
607C2×C8—732no—
608C2×C8—1462no—
609C2×C8—1462no—
610C2×C8C23×D7312yes—
611C2×C8C23×D7312yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—732no—
617C4⋊C4—732no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1461no—
629C4⋊C4—1461no—
630C4⋊C4C23×D7312yes—
631C4⋊C4C23×D7312yes—
632C22⋊C4—1464no—
633C22⋊C4—1464no—
634C42—24no—
635C42—24no—
636C42—734no—
637C42—734no—
638C42—732no—
639C42—732no—
640C42—1464no—
641C42—1464no—
642C42—1464no—
643C42—1464no—
644C42D4×D7312yes—
645C42C23×D7312yes—
646C23—734no—
647C23—732no—
648C23—1462no—
649C23—1462no—
650C23C2×D4×D7311yescharacteristic
651Q8—22no—
652Q8—24no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—2928no—
657Q8—2922no—
658Q8—734no—
659Q8—14616no—
660Q8—1462no—
661Q8—1462no—
662Q8—1462no—
663Q8—1464no—
664Q8C2×#1192402814yes—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—2928no—
676C2×C4—2922no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—734no—
680C2×C4—732no—
681C2×C4—732no—
682C2×C4—732no—
683C2×C4—1468no—
684C2×C4—1468no—
685C2×C4—14616no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1464no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1464no—
696C2×C4C2×D4×D7312yes—
697C2×C4C2×D4×D7312yes—
698C2×C4C2×D4×D7311yescharacteristic
699C2×C4#41×D7312yes—
700C2×C4C2×#1192402812yes—
701C2×C4C24×D7311yescharacteristic
702C8—22no—
703C8—22no—
704C8—1462no—
705C8—1462no—
706C22—734no—
707C22—1468no—
708C22—1462no—
709C22—1462no—
710C22#1798909612yes—
711C22#137×D7312yes—
712C22#137×D7312yes—
713C22C22×D4×D7311yescharacteristic
714C4—22no—
715C4—22no—
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—2922no—
721C4—2922no—
722C4—2922no—
723C4—734no—
724C4—1462no—
725C4—1462no—
726C4—1464no—
727C4#1798909612yes—
728C4C2×#41×D7311yescharacteristic
729C4C22×#1192402811yescharacteristic
730C2—1464no—
731C2#2262005914yesdirect product factor
732C2C2×#1798909611yescharacteristic
733C2C2×#137×D7311yescharacteristic
734C2C2×#137×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#441×C73C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenterC2×#441D73
hypocenterC73C2×#3113
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #22620059C2direct (N × H)
6. C2×#17988871C2semidirect
7. C2×#17988870C2semidirect
8. C2×#17988796C2semidirect
9. C2×#17988795C2semidirect
12. C2×#17988695C2semidirect
13. C2×#17988692C2semidirect
14. C2×#17988692C2semidirect
16. C2×#441×C73C2semidirect
45. #17988871C22semidirect
46. #17988870C22semidirect
47. #17988796C22semidirect
48. #17988795C22semidirect
51. #17988695C22semidirect
52. #17988692C22semidirect
53. #17988692C22semidirect
72. #441×C73C22semidirect
363. C2×C73#3113semidirect
382. C2×#441D73semidirect
384. C73C2×#3113semidirect
425. #441C2×D73semidirect
731. C2#22620059direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891412
C2×C4×Q8×D732
#226200592
C2×#179889192
C2×#179889162
C2×#179888712
C2×#179888702
C2×#179887962
C2×#179887952
C2×#179887442
C2×#179887412
C2×#179886952
C2×#179886922
C2×#179886422
C2×#441×C732
C2×#311373