Finite Group Databasebeta

← C2×#22622959 #33966949

Subgroups — C2×#22622959 #33966949

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989312C211yesmaximal, characteristic, complemented
2C2×#17989306C211yesmaximal, characteristic
3#22622959C2116yesmaximal, direct product factor
4C2×#17988978C211yesmaximal, characteristic
5C2×#17988965C211yesmaximal, characteristic, complemented
6C2×#17988807C211yesmaximal, characteristic
7C2×#17988806C211yesmaximal, characteristic
8C2×#17988795C211yesmaximal, characteristic, complemented
9C2×#17988795C211yesmaximal, characteristic, complemented
10C2×#17988794C211yesmaximal, characteristic, complemented
11C2×#17988790C211yesmaximal, characteristic
12C2×#17988715C211yesmaximal, characteristic, complemented
13C2×#17988695C211yesmaximal, characteristic, complemented
14C2×#17988694C211yesmaximal, characteristic, complemented
15C2×SD16×Dic73C211yesmaximal, characteristic
16C2×#497×C73C211yesmaximal, characteristic
17C22×Dic292C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924016C2211yescharacteristic
22#17989312—24no—
23#17989312C2218yescomplemented
24#17989306—24no—
25#17989306C2218yes—
26C2×#14556589C2211yescharacteristic
27C2×#14556589C2211yescharacteristic
28C2×#14556589C2211yescharacteristic
29C2×#14556584—21no—
30C2×#14556584—21no—
31C2×#14556582—21no—
32C2×#14556581—21no—
33C2×#14556581—21no—
34C2×#14556578C2211yescharacteristic
35C2×#14556568—21no—
36C2×Q8×Dic73C2211yescharacteristic
37C2×Q8×Dic73C2211yescharacteristic
38C2×Q8×Dic73C2211yescharacteristic
39C2×C4×Dic146C2211yescharacteristic
40C2×C4×Dic146C2211yescharacteristic
41C2×C4×Dic146C2211yescharacteristic
42C2×#14556556—21no—
43C2×D4×Dic73C2211yescharacteristic
44C2×#14556547—21no—
45#17988978C2218yes—
46#17988965C2218yescomplemented
47#17988807C2218yes—
48#17988806C2218yes—
49#17988795C2218yescomplemented
50#17988795C2218yescomplemented
51#17988794C2218yescomplemented
52#17988790C2218yes—
53#17988715C2218yescomplemented
54#17988695C2218yescomplemented
55#17988694C2218yescomplemented
56SD16×Dic73C2218yes—
57C2×#14556523C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556515C2211yescharacteristic
66C2×#14556512C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C22×SD16×C73C2211yescharacteristic
72C22×SD16×C73C2211yescharacteristic
73C2×C4⋊Q8×C73C2211yescharacteristic
74C2×#124×C73C2211yescharacteristic
75#497×C73C2218yes—
76C2×#97×C73C2211yescharacteristic
77C22×Dic146D411yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C23×Dic73—21no—
81C2×Dic292—24no—
82C2×Dic292C2314yes—
83C2×#11924018—42no—
84C2×#11924018—42no—
85C2×#11924018—42no—
86C2×#11924018C2314yes—
87C2×#11924018C2314yes—
88C2×#11924018C2314yes—
89C2×#11924016—42no—
90C2×#11924016C2314yes—
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93#14556589—22no—
94#14556589—22no—
95#14556589—22no—
96#14556589C2314yes—
97#14556589C2314yes—
98#14556589C2314yes—
99#14556584—28no—
100#14556584—28no—
101#14556582—28no—
102#14556581—28no—
103#14556581—28no—
104#14556578—22no—
105#14556578C2314yes—
106#14556568—28no—
107Q8×Dic73—22no—
108Q8×Dic73—22no—
109Q8×Dic73—22no—
110Q8×Dic73C2314yes—
111Q8×Dic73C2314yes—
112Q8×Dic73C2314yes—
113C4×Dic146—22no—
114C4×Dic146—22no—
115C4×Dic146D414yes—
116C4×Dic146C2314yes—
117C4×Dic146C2314yes—
118C4×Dic146C2314yes—
119#14556556—28no—
120D4×Dic73—22no—
121D4×Dic73C2314yes—
122#14556547—28no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73D411yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007D411yescharacteristic
138C2×#11924007D411yescharacteristic
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73—21no—
147C2×C4×Dic73C2311yescharacteristic
148C2×C4×Dic73C2311yescharacteristic
149#14556523C2314yes—
150C4⋊#10596831C2314yes—
151#14556520C2314yes—
152#14556520C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556515C2314yes—
156#14556515C2314yes—
157#14556515C2314yes—
158#14556512C2314yes—
159#14556501C2314yes—
160C8×Dic73C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C22×Q8×C73C2311yescharacteristic
164C22×D4×C73C2311yescharacteristic
165C2×Q16×C73—24no—
166C2×Q16×C73—42no—
167C2×Q16×C73C2314yes—
168C2×Q16×C73C2314yes—
169C2×SD16×C73—24no—
170C2×SD16×C73—42no—
171C2×SD16×C73C2314yes—
172C2×SD16×C73C2314yes—
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2311yescharacteristic
175C4⋊Q8×C73—22no—
176C4⋊Q8×C73C2314yes—
177#124×C73—22no—
178#124×C73C2314yes—
179C2×C4⋊C4×C73—21no—
180C2×C4⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182C2×C22⋊C4×C73—21no—
183C2×C42×C73C2311yescharacteristic
184#97×C73C2314yes—
185C2×Dic146—24no—
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—21no—
191C2×Dic146—21no—
192C2×Dic146C2×D414yes—
193C2×Dic146C2412yes—
194C2×Dic146C2412yes—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—24no—
200C22×Dic73—44no—
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205Dic292—28no—
206#11924018—44no—
207#11924018—44no—
208#11924018—44no—
209#11924016—44no—
210C2×#10596831—22no—
211C2×#10596831—22no—
212C2×#10596831C2412yes—
213C2×#10596831C2412yes—
214C4⋊Dic73—21no—
215C4⋊Dic73—21no—
216C4⋊Dic73—24no—
217C4⋊Dic73—24no—
218C4⋊Dic73—24no—
219C4⋊Dic73C2×D414yes—
220C4⋊Dic73C2412yes—
221C4⋊Dic73C2412yes—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007C2×D414yes—
231#11924007C2×D414yes—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234C22⋊Dic73—24no—
235C4×Dic73—24no—
236C4×Dic73—24no—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73—24no—
240C4×Dic73C2×D412yes—
241C4×Dic73C2×D412yes—
242C4×Dic73C2412yes—
243C4×Dic73C2412yes—
244C24×C73—21no—
245C2×Q8×C73—21no—
246C2×Q8×C73—21no—
247C2×Q8×C73—21no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73—22no—
251C2×Q8×C73—22no—
252C2×Q8×C73—22no—
253C2×Q8×C73—22no—
254C2×Q8×C73C2412yes—
255C2×Q8×C73C2412yes—
256C2×Q8×C73C2412yes—
257C2×D4×C73—21no—
258C2×D4×C73—22no—
259C2×D4×C73—22no—
260C2×D4×C73C2412yes—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2411yescharacteristic
267Q16×C73—28no—
268Q16×C73—44no—
269SD16×C73—28no—
270SD16×C73—44no—
271C2×C8×C73—22no—
272C2×C8×C73#4114yes—
273C2×C8×C73C2412yes—
274C2×C8×C73C2412yes—
275C4⋊C4×C73—24no—
276C4⋊C4×C73—24no—
277C22⋊C4×C73—24no—
278C22⋊C4×C73—24no—
279C42×C73C2×D412yes—
280C42×C73C2412yes—
281C23×C73—22no—
282C23×C73—42no—
283C23×C73—42no—
284C23×C73—42no—
285C23×C73C22×D411yescharacteristic
286Q8×C73—22no—
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—42no—
293Q8×C73—42no—
294Q8×C73—42no—
295D4×C73—22no—
296D4×C73—22no—
297D4×C73—42no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—42no—
304C2×C4×C73—42no—
305C2×C4×C73—42no—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D412yes—
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C2×#4112yes—
310C2×C4×C73H(5,𝔽2)12yes—
311C2×C4×C73C2511yescharacteristic
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—48no—
324C2×Dic73#13714yes—
325C2×Dic73C22×D412yes—
326C2×Dic73C22×D412yes—
327C2×Dic73C22×D412yes—
328C2×Dic73C22×D412yes—
329Dic146—28no—
330Dic146—22no—
331Dic146—22no—
332Dic146—22no—
333Dic146—22no—
334Dic146—42no—
335Dic146—42no—
336C8×C73—22no—
337C8×C73C2×#4114yes—
338#10596831—22no—
339#10596831—22no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—84no—
344C22×C73#55012yes—
345C22×C73C2×#13712yes—
346C22×C73#57812yes—
347C22×C73C23×D411yescharacteristic
348C4×C73—22no—
349C4×C73—22no—
350C4×C73—42no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73#55012yes—
354C4×C73C22×#4111yescharacteristic
355C4×C73C2×H(5,𝔽2)11yescharacteristic
356Dic73—22no—
357Dic73—22no—
358Dic73—22no—
359Dic73—42no—
360Dic73—42no—
361Dic73—42no—
362Dic73—42no—
363Dic73C2×#13714yes—
364C2×#3398—731nomaximal, Sylow
365C2×C73—82no—
366C2×C73#339814yescomplemented
367C2×C73C2×#55011yescharacteristic
368C2×C73C22×#13711yescharacteristic
369C2×C73C2×#57811yescharacteristic
370C2×#557—731no—
371C2×#556—731no—
372#3398—7316no—
373C2×#497—731no—
374C2×#497D7311yescharacteristic
375C2×#494—731no—
376C2×#464—731no—
377C2×#464—731no—
378C2×#462—731no—
379C2×#462—731no—
380C2×#462—731no—
381C2×#461—731no—
382C2×#446—731no—
383C2×#441—731no—
384C2×#441—731no—
385C2×C4×SD16—731no—
386C73C2×#339811yescharacteristic, complemented, Sylow
387C22×Q16—731no—
388C22×Q16—731no—
389C22×Q16—731no—
390C22×Q16—731no—
391C22×Q16C2×D7311yescharacteristic
392C22×Q16C2×D7311yescharacteristic
393C22×SD16—731no—
394C22×SD16C2×D7311yescharacteristic
395C22×SD16C2×D7311yescharacteristic
396#557—738no—
397#557—1464no—
398#556—738no—
399#556—1464no—
400C2×C4⋊Q8—731no—
401C2×C4⋊Q8—731no—
402C2×C4⋊Q8—731no—
403C2×C4⋊Q8C2×D7311yescharacteristic
404C2×#126—1461no—
405C2×#126—1461no—
406C2×#125—1461no—
407C2×#125—1461no—
408C2×#125—1461no—
409C2×#124—731no—
410C2×#124C2×D7311yescharacteristic
411C2×C22⋊Q8—1461no—
412C2×C4×Q8—731no—
413C2×C4×Q8—731no—
414C2×C4×Q8—731no—
415C2×C4×Q8—731no—
416C2×C4×Q8—731no—
417C2×C4×Q8—731no—
418C2×C4×Q8—1461no—
419C2×C4×D4—731no—
420C2×#117—1461no—
421#497—738no—
422#497C2×D7318yes—
423#494—738no—
424#464—738no—
425#464—738no—
426#462—738no—
427#462—738no—
428#462—738no—
429#461—738no—
430#446—738no—
431#441—738no—
432#441—738no—
433C4×SD16—738no—
434C2×#106—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×C4⋊C8—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103—731no—
443C2×#102—731no—
444C2×#97—731no—
445C2×#97C2×D7311yescharacteristic
446C2×C4×C8—731no—
447C22×Q8—731no—
448C22×Q8—731no—
449C22×Q8—731no—
450C22×Q8C22×D7311yescharacteristic
451C22×Q8C22×D7311yescharacteristic
452C22×Q8C22×D7311yescharacteristic
453C22×D4C22×D7311yescharacteristic
454C23×C4—1461no—
455C2×Q16—24no—
456C2×Q16—42no—
457C2×Q16—2922no—
458C2×Q16—2922no—
459C2×Q16—2922no—
460C2×Q16—734no—
461C2×Q16—734no—
462C2×Q16—734no—
463C2×Q16—734no—
464C2×Q16—1464no—
465C2×Q16C22×D7314yes—
466C2×Q16C22×D7314yes—
467C2×SD16—24no—
468C2×SD16—42no—
469C2×SD16—2922no—
470C2×SD16—734no—
471C2×SD16C22×D7314yes—
472C2×SD16C22×D7314yes—
473C22×C8—731no—
474C22×C8—731no—
475C22×C8C22×D7311yescharacteristic
476C22×C8C22×D7311yescharacteristic
477C4⋊Q8—22no—
478C4⋊Q8—734no—
479C4⋊Q8—734no—
480C4⋊Q8—734no—
481C4⋊Q8—1462no—
482C4⋊Q8—1462no—
483C4⋊Q8—1462no—
484C4⋊Q8C22×D7314yes—
485#126—1468no—
486#126—1468no—
487#125—1468no—
488#125—1468no—
489#125—1468no—
490#124—22no—
491#124—734no—
492#124—1462no—
493#124C22×D7314yes—
494C22⋊Q8—1468no—
495C4×Q8—734no—
496C4×Q8—734no—
497C4×Q8—734no—
498C4×Q8—734no—
499C4×Q8—734no—
500C4×Q8—734no—
501C4×Q8—734no—
502C4×Q8—1462no—
503C4×Q8—1462no—
504C4×Q8—1462no—
505C4×Q8—1468no—
506C4×Q8—1462no—
507C4×Q8—1462no—
508C4×D4—734no—
509C4×D4—1462no—
510#117—1468no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C42—731no—
535C2×C42—731no—
536C2×C42—1461no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42—1461no—
540C2×C42—1461no—
541C2×C42C22×D7311yescharacteristic
542#106—734no—
543C4⋊C8—734no—
544C4⋊C8—734no—
545C4⋊C8—734no—
546#103—734no—
547#103—734no—
548#103—734no—
549#103—734no—
550#103—734no—
551#102—734no—
552#97—734no—
553#97C22×D7314yes—
554C4×C8—734no—
555C24—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—734no—
566C2×Q8—732no—
567C2×Q8—732no—
568C2×Q8—1464no—
569C2×Q8—1462no—
570C2×Q8—1462no—
571C2×Q8—1462no—
572C2×Q8—1462no—
573C2×Q8—1461no—
574C2×Q8—1461no—
575C2×Q8C23×D7312yes—
576C2×Q8C23×D7312yes—
577C2×Q8C23×D7312yes—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4C23×D7312yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—2924no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—731no—
590C22×C4—1464no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4D4×D7311yescharacteristic
596C22×C4D4×D7311yescharacteristic
597C22×C4C23×D7311yescharacteristic
598Q16—28no—
599Q16—44no—
600Q16—2924no—
601Q16—2924no—
602Q16—2924no—
603Q16—1468no—
604SD16—28no—
605SD16—44no—
606SD16—2924no—
607C2×C8—22no—
608C2×C8—732no—
609C2×C8—732no—
610C2×C8—1462no—
611C2×C8—1462no—
612C2×C8#1192402714yes—
613C2×C8C23×D7312yes—
614C2×C8C23×D7312yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—734no—
618C4⋊C4—734no—
619C4⋊C4—734no—
620C4⋊C4—732no—
621C4⋊C4—732no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1461no—
634C4⋊C4—1461no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C22⋊C4—1464no—
640C42—732no—
641C42—732no—
642C42—732no—
643C42—732no—
644C42—1464no—
645C42—1464no—
646C42—1464no—
647C42—1464no—
648C42—1464no—
649C42D4×D7312yes—
650C42C23×D7312yes—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×D4×D7311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—2922no—
666Q8—2922no—
667Q8—1468no—
668Q8—1462no—
669Q8—1462no—
670Q8—1462no—
671Q8—1462no—
672D4—22no—
673D4—22no—
674D4—42no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—2922no—
686C2×C4—2922no—
687C2×C4—2928no—
688C2×C4—734no—
689C2×C4—732no—
690C2×C4—732no—
691C2×C4—732no—
692C2×C4—732no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4C2×#1192402712yes—
704C2×C4#1455663612yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—1462no—
708C8—1462no—
709C8C2×#1192402714yes—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22#1798925712yes—
715C22#137×D7312yes—
716C22#1798940312yes—
717C22C22×D4×D7311yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—2922no—
724C4—2922no—
725C4—2922no—
726C4—2922no—
727C4—734no—
728C4—1462no—
729C4—1462no—
730C4—1462no—
731C4#1798925712yes—
732C4C22×#1192402711yescharacteristic
733C4C2×#1455663611yescharacteristic
734C2—82no—
735C2#2262295914yesdirect product factor
736C2C2×#1798925711yescharacteristic
737C2C2×#137×D7311yescharacteristic
738C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#497×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenterC2×#497D73
hypocenterC73C2×#3398
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#17989312C2semidirect
3. #22622959C2direct (N × H)
5. C2×#17988965C2semidirect
8. C2×#17988795C2semidirect
9. C2×#17988795C2semidirect
10. C2×#17988794C2semidirect
12. C2×#17988715C2semidirect
13. C2×#17988695C2semidirect
14. C2×#17988694C2semidirect
23. #17989312C22semidirect
46. #17988965C22semidirect
49. #17988795C22semidirect
50. #17988795C22semidirect
51. #17988794C22semidirect
53. #17988715C22semidirect
54. #17988695C22semidirect
55. #17988694C22semidirect
366. C2×C73#3398semidirect
386. C73C2×#3398semidirect
735. C2#22622959direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893122
C2×#179893062
#226229592
C2×#179889782
C2×#179889652
C2×#179888072
C2×#179888062
C2×#179887952
C2×#179887942
C2×#179887902
C2×#179887152
C2×#179886952
C2×#179886942
C2×SD16×Dic732
C2×#497×C732
C2×#339873