Finite Group Databasebeta

← C2×#22620159 #33954262

Subgroups — C2×#22620159 #33954262

Order 18688.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989206C211yesmaximal, characteristic
2C2×#17989063C211yesmaximal, characteristic, complemented
3#22620159C2116yesmaximal, direct product factor
4C2×#17988927C211yesmaximal, characteristic, complemented
5C2×#17988909C211yesmaximal, characteristic
6C2×#17988883C211yesmaximal, characteristic, complemented
7C2×#17988872C211yesmaximal, characteristic, complemented
8C2×#17988806C211yesmaximal, characteristic, complemented
9C2×#17988741C211yesmaximal, characteristic, complemented
10C2×#17988724C211yesmaximal, characteristic
11C2×#17988691C211yesmaximal, characteristic, complemented
12C2×#17988688C211yesmaximal, characteristic, complemented
13C2×Q16×Dic73C211yesmaximal, characteristic, complemented
14C2×#17988678C211yesmaximal, characteristic, complemented
15C2×#17988647C211yesmaximal, characteristic, complemented
16C2×#464×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20#17989206—24no—
21#17989206C2218yes—
22C2×#14556591C2211yescharacteristic
23C2×#14556584—21no—
24C2×#14556577—21no—
25C2×#14556575—21no—
26C2×#14556568—21no—
27C2×#14556567C2211yescharacteristic
28C2×#14556562C2211yescharacteristic
29#17989063—24no—
30#17989063C2218yescomplemented
31C2×Q8×Dic73C2211yescharacteristic
32C2×Q8×Dic73C2211yescharacteristic
33C2×C4×Dic146—21no—
34C2×C4×Dic146C2211yescharacteristic
35C2×#14556556—21no—
36C2×#14556556C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×#14556549—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556548—21no—
41C2×#14556548C2211yescharacteristic
42#17988927C2218yescomplemented
43#17988909C2218yes—
44#17988883C2218yescomplemented
45#17988872C2218yescomplemented
46#17988806C2218yescomplemented
47#17988741C2218yescomplemented
48#17988724C2218yes—
49#17988691C2218yescomplemented
50#17988688C2218yescomplemented
51Q16×Dic73C2218yescomplemented
52#17988678C2218yescomplemented
53#17988647C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556525C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556503C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C2×#124×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#464×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C2×Q8×D73—24no—
81C2×Q8×D73—22no—
82C2×Q8×D73—24no—
83C2×Q8×D73C2314yes—
84C22×C22⋊D73—21no—
85C23×Dic73—21no—
86C22×C4×D73—21no—
87C22×C4×D73C2311yescharacteristic
88C2×#11924018—24no—
89C2×#11924018C2314yes—
90C2×#11924016—24no—
91C2×#11924016C2314yes—
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94#14556591—22no—
95#14556591C2314yes—
96#14556584—28no—
97#14556577—28no—
98#14556575—28no—
99#14556568—28no—
100#14556567—22no—
101#14556567C2314yes—
102#14556562—22no—
103#14556562C2314yes—
104Q8×Dic73—22no—
105Q8×Dic73—22no—
106Q8×Dic73C2314yes—
107Q8×Dic73C2314yes—
108C4×Dic146—28no—
109C4×Dic146—22no—
110C4×Dic146C2314yes—
111#14556556—28no—
112#14556556—22no—
113#14556556C2314yes—
114D4×Dic73—22no—
115D4×Dic73C2314yes—
116#14556549—22no—
117#14556549—28no—
118#14556549C2314yes—
119#14556548—28no—
120#14556548D414yes—
121#14556548C2314yes—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005D411yescharacteristic
138C2×#11924005D411yescharacteristic
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yes—
146#14556525C2314yes—
147#14556522C2314yes—
148#14556522C2314yes—
149C4⋊#10596831C2314yes—
150#14556516C2314yes—
151#14556516C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556512C2314yes—
156#14556503C2314yes—
157#14556503C2314yes—
158#14556501C2314yes—
159C8×Dic73C2314yes—
160C22×Q8×C73C2311yescharacteristic
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73C2314yes—
165C2×SD16×C73—24no—
166C2×SD16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169#124×C73—22no—
170#124×C73C2314yes—
171C4×Q8×C73—22no—
172C4×Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C42×C73—21no—
178C2×C42×C73C2311yescharacteristic
179C4⋊C8×C73C2314yes—
180#103×C73C2314yes—
181#102×C73C2314yes—
182C23×D73C2×D411yescharacteristic
183C2×Dic146—28no—
184C2×Dic146—21no—
185C2×Dic146—22no—
186C2×Dic146—24no—
187C2×Dic146—24no—
188C2×Dic146—82no—
189C2×Dic146#4114yes—
190C2×Dic146C2412yes—
191Q8×D73—216no—
192Q8×D73—28no—
193Q8×D73—28no—
194C2×C22⋊D73—24no—
195C2×C22⋊D73—82no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—24no—
201C22×Dic73—82no—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C2×C4×D73—28no—
206C2×C4×D73—24no—
207C2×C4×D73—22no—
208C2×C4×D73—22no—
209C2×C4×D73C2×D412yes—
210C2×C4×D73C2412yes—
211#11924018—28no—
212#11924016—28no—
213C2×#10596831—22no—
214C2×#10596831—22no—
215C2×#10596831C2412yes—
216C2×#10596831C2412yes—
217C4⋊Dic73—24no—
218C4⋊Dic73—21no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73—24no—
222C4⋊Dic73—24no—
223C4⋊Dic73C2412yes—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007C2×D414yes—
230#11924007C2×D414yes—
231C22⋊Dic73—24no—
232C22⋊Dic73—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005C2×D414yes—
236#11924005C2×D414yes—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73—24no—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C4×Dic73C2×D412yes—
243C4×Dic73C2412yes—
244C24×C73—21no—
245C2×Q8×C73—21no—
246C2×Q8×C73—21no—
247C2×Q8×C73—22no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73#4114yes—
251C2×Q8×C73C2412yes—
252C2×Q8×C73C2412yes—
253C2×D4×C73—21no—
254C2×D4×C73—22no—
255C2×D4×C73—22no—
256C2×D4×C73C2412yes—
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—
264SD16×C73—28no—
265C2×C8×C73—22no—
266C2×C8×C73—22no—
267C2×C8×C73C2412yes—
268C2×C8×C73C2412yes—
269C4⋊C4×C73—24no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73C2412yes—
272C22⋊C4×C73—24no—
273C22⋊C4×C73—24no—
274C42×C73—24no—
275C42×C73C2×D412yes—
276C42×C73C2412yes—
277C23×C73—22no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73C22×D411yescharacteristic
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73C22×D412yes—
286Q8×C73—24no—
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—22no—
290Q8×C73—42no—
291Q8×C73C2×#4114yes—
292D4×C73—22no—
293D4×C73—22no—
294D4×C73—42no—
295C2×C4×C73—24no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4112yes—
307C2×C4×C73C2×#4112yes—
308C2×C4×C73C2511yescharacteristic
309C22⋊D73—84no—
310C2×Dic73—24no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—84no—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C2×Dic73C22×D412yes—
325C4×D73—216no—
326C4×D73—24no—
327C4×D73—22no—
328C4×D73—22no—
329Dic146—216no—
330Dic146—24no—
331Dic146—22no—
332Dic146—84no—
333Dic146C2×#4114yes—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831—22no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—84no—
342C22×C73#52512yes—
343C22×C73#57712yes—
344C22×C73#57812yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—44no—
350C4×C73—24no—
351C4×C73—22no—
352C4×C73—22no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73#52512yes—
356C4×C73C22×#4111yescharacteristic
357C4×C73C22×#4111yescharacteristic
358Dic73—22no—
359Dic73—24no—
360Dic73—22no—
361Dic73—22no—
362Dic73—42no—
363Dic73—42no—
364Dic73—42no—
365C2×#3121—731nomaximal, Sylow
366C2×C73—82no—
367C2×C73#312114yescomplemented
368C2×C73C2×#52511yescharacteristic
369C2×C73C2×#57711yescharacteristic
370C2×C73C2×#57811yescharacteristic
371D73—42no—
372C2×#542—731no—
373C2×#519—731no—
374#3121—7316no—
375C2×#485—731no—
376C2×#482—731no—
377C2×#477—731no—
378C2×#475—731no—
379C2×#464—731no—
380C2×#464D7311yescharacteristic, complemented
381C2×#451—731no—
382C2×#448—731no—
383C2×#441—731no—
384C2×#440—731no—
385C2×C4×Q16—731no—
386C2×C4×SD16—731no—
387C2×#433—731no—
388C73C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8—731no—
390C22×Q16—731no—
391C22×Q16C2×D7311yescharacteristic
392C22×SD16—731no—
393C22×SD16C2×D7311yescharacteristic
394#542—738no—
395#542—1464no—
396C2×C4⋊Q8—731no—
397C2×#126—1461no—
398C2×#124—1461no—
399C2×#124C2×D7311yescharacteristic
400C2×#123—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—1461no—
403C2×#121—731no—
404#519—738no—
405#519—1464no—
406C2×C4×Q8—731no—
407C2×C4×Q8—731no—
408C2×C4×Q8—731no—
409C2×C4×Q8—731no—
410C2×C4×Q8—1461no—
411C2×C4×Q8—1461no—
412C2×C4×Q8C2×D7311yescharacteristic
413C2×C4×D4—731no—
414C2×#117—731no—
415C2×#117—731no—
416C2×#117—1461no—
417C2×#117—1461no—
418#485—738no—
419#482—738no—
420#477—738no—
421#475—738no—
422#464—738no—
423#464C2×D7318yescomplemented
424#451—738no—
425#448—738no—
426#441—738no—
427#440—738no—
428C4×Q16—738no—
429C4×SD16—738no—
430#433—738no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#106—731no—
434C2×#106—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8C2×D7311yescharacteristic
437C2×#103—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103C2×D7311yescharacteristic
443C2×#102—731no—
444C2×#102C2×D7311yescharacteristic
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×#97—731no—
448C2×C4×C8—731no—
449C22×Q8—734no—
450C22×Q8—731no—
451C22×Q8—1461no—
452C22×Q8—1462no—
453C22×Q8—1464no—
454C22×Q8—1464no—
455C22×Q8—1461no—
456C22×Q8C22×D7311yescharacteristic
457C22×Q8C22×D7311yescharacteristic
458C22×D4—1461no—
459C22×D4C22×D7311yescharacteristic
460C23×C4—731no—
461C23×C4—1461no—
462C23×C4—1461no—
463C2×Q16—24no—
464C2×Q16—734no—
465C2×Q16—1464no—
466C2×Q16C22×D7314yes—
467C2×SD16—24no—
468C2×SD16—734no—
469C2×SD16—1464no—
470C2×SD16C22×D7314yes—
471C22×C8—731no—
472C22×C8—731no—
473C22×C8C22×D7311yescharacteristic
474C22×C8C22×D7311yescharacteristic
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477#126—1468no—
478#124—22no—
479#124—1468no—
480#124C22×D7314yes—
481#123—1468no—
482C22⋊Q8—734no—
483C22⋊Q8—1468no—
484C22⋊Q8—1462no—
485#121—734no—
486#121—1462no—
487C4×Q8—22no—
488C4×Q8—734no—
489C4×Q8—734no—
490C4×Q8—734no—
491C4×Q8—734no—
492C4×Q8—1468no—
493C4×Q8—1462no—
494C4×Q8—1462no—
495C4×Q8—1462no—
496C4×Q8—1468no—
497C4×Q8—1462no—
498C4×Q8C22×D7314yes—
499C4×D4—734no—
500C4×D4—1462no—
501#117—734no—
502#117—734no—
503#117—734no—
504#117—1468no—
505#117—1468no—
506#117—1462no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—21no—
529C2×C42—731no—
530C2×C42—1461no—
531C2×C42—1461no—
532C2×C42—1461no—
533C2×C42—1461no—
534C2×C42—1461no—
535C2×C42C22×D7311yescharacteristic
536#107—734no—
537#107—734no—
538#106—734no—
539#106—734no—
540C4⋊C8—734no—
541C4⋊C8C22×D7314yes—
542#103—734no—
543#103—734no—
544#103—734no—
545#103—734no—
546#103—734no—
547#103C22×D7314yes—
548#102—734no—
549#102C22×D7314yes—
550C22⋊C8—734no—
551C22⋊C8—734no—
552#97—734no—
553C4×C8—734no—
554C24—21no—
555C24—731no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—5842no—
562C2×Q8—734no—
563C2×Q8—732no—
564C2×Q8—1464no—
565C2×Q8—1468no—
566C2×Q8—1468no—
567C2×Q8—14616no—
568C2×Q8—1468no—
569C2×Q8—1464no—
570C2×Q8—1461no—
571C2×Q8—1462no—
572C2×Q8#1192402714yes—
573C2×Q8C23×D7312yes—
574C2×Q8C23×D7312yes—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—5842no—
579C2×D4—1464no—
580C2×D4C23×D7312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—5842no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—732no—
589C22×C4—732no—
590C22×C4—1464no—
591C22×C4—1468no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1464no—
596C22×C4—1461no—
597C22×C4—1462no—
598C22×C4—1462no—
599C22×C4D4×D7311yescharacteristic
600C22×C4D4×D7311yescharacteristic
601C22×C4C23×D7311yescharacteristic
602Q16—28no—
603Q16—1468no—
604SD16—28no—
605SD16—1468no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—732no—
609C2×C8—732no—
610C2×C8—1462no—
611C2×C8—1462no—
612C2×C8C23×D7312yes—
613C2×C8C23×D7312yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—734no—
617C4⋊C4—734no—
618C4⋊C4—732no—
619C4⋊C4—732no—
620C4⋊C4—732no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1461no—
627C4⋊C4—1461no—
628C4⋊C4—1461no—
629C4⋊C4—1464no—
630C4⋊C4C23×D7312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—734no—
634C22⋊C4—734no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—24no—
640C42—732no—
641C42—732no—
642C42—1464no—
643C42—1464no—
644C42—1464no—
645C42—1464no—
646C42—1464no—
647C42D4×D7312yes—
648C42C23×D7312yes—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—732no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23C2×D4×D7311yescharacteristic
658Q8—22no—
659Q8—24no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—5844no—
664Q8—734no—
665Q8—14616no—
666Q8—1462no—
667Q8—1464no—
668Q8C2×#1192402714yes—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—5844no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—2922no—
682C2×C4—2922no—
683C2×C4—2922no—
684C2×C4—5844no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—732no—
688C2×C4—14616no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1464no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1464no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4#41×D7312yes—
704C2×C4C2×#1192402712yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1462no—
709C8—1462no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—2924no—
715C22—1462no—
716C22—1462no—
717C22—1462no—
718C22#1798909712yes—
719C22#1798939612yes—
720C22#1798940112yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—2922no—
728C4—2922no—
729C4—2922no—
730C4—1462no—
731C4—1462no—
732C4—1462no—
733C4—1464no—
734C4#1798909712yes—
735C4C2×#41×D7311yescharacteristic
736C4C22×#1192402711yescharacteristic
737C2—82no—
738C2—2922no—
739C2#2262015914yesdirect product factor
740C2C2×#1798909711yescharacteristic
741C2C2×#1798939611yescharacteristic
742C2C2×#1798940111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#464×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556562C22
hypercenterC2×#464D73
hypocenterC73C2×#3121
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×#17989063C2semidirect
3. #22620159C2direct (N × H)
4. C2×#17988927C2semidirect
6. C2×#17988883C2semidirect
7. C2×#17988872C2semidirect
8. C2×#17988806C2semidirect
9. C2×#17988741C2semidirect
11. C2×#17988691C2semidirect
12. C2×#17988688C2semidirect
13. C2×Q16×Dic73C2semidirect
14. C2×#17988678C2semidirect
15. C2×#17988647C2semidirect
16. C2×#464×C73C2semidirect
30. #17989063C22semidirect
42. #17988927C22semidirect
44. #17988883C22semidirect
45. #17988872C22semidirect
46. #17988806C22semidirect
47. #17988741C22semidirect
49. #17988691C22semidirect
50. #17988688C22semidirect
51. Q16×Dic73C22semidirect
52. #17988678C22semidirect
53. #17988647C22semidirect
73. #464×C73C22semidirect
367. C2×C73#3121semidirect
380. C2×#464D73semidirect
388. C73C2×#3121semidirect
423. #464C2×D73semidirect
739. C2#22620159direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892062
C2×#179890632
#226201592
C2×#179889272
C2×#179889092
C2×#179888832
C2×#179888722
C2×#179888062
C2×#179887412
C2×#179887242
C2×#179886912
C2×#179886882
C2×Q16×Dic732
C2×#179886782
C2×#179886472
C2×#464×C732
C2×#312173