Finite Group Databasebeta

← C2×#22621802 #33962374

Subgroups — C2×#22621802 #33962374

Order 18688.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989295C211yesmaximal, characteristic
2C2×#17989250C211yesmaximal, characteristic
3#22621802C2116yesmaximal, direct product factor
4C2×#17988936C211yesmaximal, characteristic, complemented
5C2×#17988924C211yesmaximal, characteristic, complemented
6C2×#17988920C211yesmaximal, characteristic, complemented
7C2×#17988881C211yesmaximal, characteristic, complemented
8C2×#17988827C211yesmaximal, characteristic, complemented
9C2×#17988795C211yesmaximal, characteristic, complemented
10C2×#17988742C211yesmaximal, characteristic, complemented
11C2×#17988741C211yesmaximal, characteristic, complemented
12C2×#17988679C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D73C211yesmaximal, characteristic
14C22×#14556516C211yesmaximal, characteristic, complemented
15C2×#103×D73C211yesmaximal, characteristic, complemented
16C2×#467×C73C211yesmaximal, characteristic, complemented
17C23×Dic146C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×C8×D73C2211yescharacteristic
22#17989295—24no—
23#17989295C2218yes—
24#17989250—24no—
25#17989250C2218yes—
26C2×#14556590—21no—
27C2×#14556590C2211yescharacteristic
28C2×#14556589C2211yescharacteristic
29C2×#14556581—21no—
30C2×#14556571—21no—
31C2×#14556571C2211yescharacteristic
32C2×#14556569—21no—
33C2×#14556568—21no—
34C2×#14556568—21no—
35C2×#14556567C2211yescharacteristic
36C2×Q8×Dic73C2211yescharacteristic
37C2×#14556556C2211yescharacteristic
38C2×C4×C22⋊D73C2211yescharacteristic
39C2×#14556551—21no—
40C2×#14556551—21no—
41C22×C4⋊Dic73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988936C2218yescomplemented
44#17988924C2218yescomplemented
45#17988920C2218yescomplemented
46#17988881C2218yescomplemented
47#17988827C2218yescomplemented
48#17988795C2218yescomplemented
49#17988742C2218yescomplemented
50#17988741C2218yescomplemented
51#17988679C2218yescomplemented
52C8×C22⋊D73C2218yes—
53C2×#14556524C2211yescharacteristic
54C2×#14556524C2211yescharacteristic
55C2×#14556520C2211yescharacteristic
56C2×#14556516C2211yescharacteristic
57C2×#14556516C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2218yescomplemented
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65#103×D73C2218yescomplemented
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×C22⋊Q8×C73C2211yescharacteristic
73#467×C73C2218yescomplemented
74C2×#107×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146—24no—
80C22×Dic146—21no—
81C22×Dic146—22no—
82C22×Dic146—42no—
83C22×Dic146C2311yescharacteristic
84C22×Dic146C2314yes—
85C22×Dic146C2311yescharacteristic
86C2×Q8×D73—22no—
87C2×Q8×D73—24no—
88C2×Q8×D73—42no—
89C2×Q8×D73C2314yes—
90C22×C22⋊D73D411yescharacteristic
91C23×Dic73—21no—
92C23×Dic73—21no—
93C22×C4×D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73C2311yescharacteristic
96C2×#11924018—24no—
97C2×#11924018—42no—
98C2×#11924018C2314yes—
99C2×#11924018C2314yes—
100C22×#10596831C2311yescharacteristic
101C22×#10596831C2311yescharacteristic
102C2×C8×D73—42no—
103C2×C8×D73C2314yes—
104#14556590—28no—
105#14556590—22no—
106#14556590C2314yes—
107#14556589—22no—
108#14556589C2314yes—
109#14556581—28no—
110#14556571—22no—
111#14556571—28no—
112#14556571C2314yes—
113#14556569—28no—
114#14556568—28no—
115#14556568—28no—
116#14556567—22no—
117#14556567C2314yes—
118Q8×Dic73—22no—
119Q8×Dic73C2314yes—
120#14556556—22no—
121#14556556C2314yes—
122C4×C22⋊D73D414yes—
123C4×C22⋊D73C2314yes—
124#14556551—28no—
125#14556551—28no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73—22no—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×C4⋊Dic73C2314yes—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007D411yescharacteristic
140C4⋊C4×D73—22no—
141C4⋊C4×D73C2314yes—
142C2×C22⋊Dic73D411yescharacteristic
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73C2311yescharacteristic
149#14556524C2314yes—
150#14556524C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556515C2314yes—
157#14556515C2314yes—
158#14556514C2314yes—
159#14556514C2314yes—
160C22⋊#10596831C2314yes—
161#14556503C2314yes—
162C8×Dic73C2314yes—
163C22×Q8×C73C2311yescharacteristic
164C22×Q8×C73C2311yescharacteristic
165C23×C4×C73C2311yescharacteristic
166C2×Q16×C73—42no—
167C2×Q16×C73C2314yes—
168C22×C8×C73—42no—
169C22×C8×C73C2311yescharacteristic
170C22×C8×C73C2311yescharacteristic
171C22×C8×C73C2314yes—
172C22⋊Q8×C73—22no—
173C22⋊Q8×C73—22no—
174C22⋊Q8×C73C2314yes—
175C22⋊Q8×C73C2314yes—
176C2×C4⋊C4×C73—21no—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C22⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182#107×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186C2×Dic146—21no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—28no—
191C2×Dic146—24no—
192C2×Dic146—21no—
193C2×Dic146—24no—
194C2×Dic146—24no—
195C2×Dic146—44no—
196C2×Dic146—48no—
197C2×Dic146—44no—
198C2×Dic146—44no—
199C2×Dic146—82no—
200C2×Dic146#4114yes—
201C2×Dic146C2412yes—
202C2×Dic146C2412yes—
203Q8×D73—28no—
204Q8×D73—44no—
205Q8×D73—48no—
206C2×C22⋊D73Q1618yescomplemented
207C2×C22⋊D73C2×D414yes—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—24no—
213C22×Dic73—24no—
214C22×Dic73—44no—
215C22×Dic73—82no—
216C22×Dic73C2×D411yescharacteristic
217C22×Dic73C2×D411yescharacteristic
218C22×Dic73C2×D411yescharacteristic
219C2×C4×D73—22no—
220C2×C4×D73—22no—
221C2×C4×D73—24no—
222C2×C4×D73—24no—
223C2×C4×D73—44no—
224C2×C4×D73—82no—
225C2×C4×D73C2×D412yes—
226C2×C4×D73C2412yes—
227#11924018—28no—
228#11924018—44no—
229C2×#10596831—22no—
230C2×#10596831—22no—
231C2×#10596831C2412yes—
232C2×#10596831C2412yes—
233C8×D73—44no—
234C4⋊Dic73—21no—
235C4⋊Dic73—21no—
236C4⋊Dic73—24no—
237C4⋊Dic73—24no—
238C4⋊Dic73—24no—
239C4⋊Dic73C2412yes—
240C4⋊Dic73C2412yes—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245#11924007—24no—
246#11924007—24no—
247#11924007C2×D414yes—
248C22⋊Dic73C2×D414yes—
249#11924005—24no—
250#11924005—24no—
251#11924005C2×D414yes—
252C4×Dic73—24no—
253C4×Dic73—24no—
254C4×Dic73C2×D412yes—
255C4×Dic73C2412yes—
256C24×C73C2×D411yescharacteristic
257C2×Q8×C73—21no—
258C2×Q8×C73—21no—
259C2×Q8×C73—22no—
260C2×Q8×C73—22no—
261C2×Q8×C73—22no—
262C2×Q8×C73—22no—
263C2×Q8×C73C2412yes—
264C2×Q8×C73C2412yes—
265C22×C4×C73—22no—
266C22×C4×C73—22no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73C2×D411yescharacteristic
272C22×C4×C73C2×D412yes—
273C22×C4×C73C2412yes—
274C22×C4×C73C2411yescharacteristic
275Q16×C73—44no—
276C2×C8×C73—22no—
277C2×C8×C73—22no—
278C2×C8×C73—44no—
279C2×C8×C73C2412yes—
280C2×C8×C73C2412yes—
281C4⋊C4×C73—24no—
282C4⋊C4×C73—24no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73—21no—
285C4⋊C4×C73C2412yes—
286C4⋊C4×C73C2412yes—
287C22⋊C4×C73—24no—
288C22⋊C4×C73—24no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73C2×Q1614yes—
292C23×C73C22×D412yes—
293C23×C73C22×D411yescharacteristic
294C22×D73—22no—
295C22×D73—22no—
296C22×D73C2×Q1614yes—
297C22×D73C22×D412yes—
298Q8×C73—22no—
299Q8×C73—22no—
300Q8×C73—22no—
301Q8×C73—22no—
302Q8×C73—42no—
303Q8×C73—42no—
304C2×C4×C73—22no—
305C2×C4×C73—24no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—42no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73C22×D412yes—
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C2×#4112yes—
319C2×C4×C73H(5,𝔽2)12yes—
320C2×C4×C73C2511yescharacteristic
321C22⋊D73C2×Q16116yescomplemented
322C2×Dic73—22no—
323C2×Dic73—24no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—48no—
330C2×Dic73—42no—
331C2×Dic73—42no—
332C2×Dic73—42no—
333C2×Dic73—84no—
334C2×Dic73C2×Q1614yes—
335C2×Dic73C22×D412yes—
336C2×Dic73C22×D412yes—
337C2×Dic73C22×D412yes—
338C4×D73—24no—
339C4×D73—22no—
340C4×D73—22no—
341C4×D73—48no—
342C4×D73—84no—
343Dic146—24no—
344Dic146—22no—
345Dic146—22no—
346Dic146—22no—
347Dic146—48no—
348Dic146—48no—
349Dic146—42no—
350Dic146—84no—
351Dic146C2×#4114yes—
352C8×C73—22no—
353C8×C73—22no—
354#10596831—22no—
355#10596831—22no—
356C22×C73—22no—
357C22×C73—28no—
358C22×C73—22no—
359C22×C73#54612yes—
360C22×C73C22×Q1614yes—
361C22×C73C22×Q1612yes—
362C22×C73#57712yes—
363C22×C73C23×D411yescharacteristic
364C2×D73—22no—
365C2×D73—28no—
366C2×D73—22no—
367C2×D73C22×Q1614yes—
368C4×C73—22no—
369C4×C73—42no—
370C4×C73—42no—
371C4×C73—42no—
372C4×C73—42no—
373C4×C73#54612yes—
374C4×C73C22×#4111yescharacteristic
375C4×C73C2×H(5,𝔽2)11yescharacteristic
376Dic73—24no—
377Dic73—22no—
378Dic73—22no—
379Dic73—42no—
380Dic73—42no—
381Dic73—42no—
382Dic73C22×Q1614yes—
383C2×#3299—731nomaximal, Sylow
384C2×C73—24no—
385C2×C73#329914yescomplemented
386C2×C73C2×#54611yescharacteristic
387C2×C73C23×Q1611yescharacteristic
388C2×C73C2×#57711yescharacteristic
389D73—24no—
390C2×#554—731no—
391C2×D4×Q8—731no—
392#3299—7316no—
393C2×#487—731no—
394C2×#484—731no—
395C2×#484—731no—
396C2×#477—731no—
397C2×#467—731no—
398C2×#467D7311yescharacteristic, complemented
399C2×#462—731no—
400C2×#451—731no—
401C2×#451—731no—
402C2×C4×Q16—731no—
403C2×C8×D4—731no—
404C22×#103—731no—
405C22×#103—731no—
406C73C2×#329911yescharacteristic, complemented, Sylow
407C23×Q8—731no—
408C23×Q8—731no—
409C22×Q16—731no—
410C22×Q16—731no—
411C22×Q16C2×D7311yescharacteristic
412C23×C8—731no—
413C23×C8C2×D7311yescharacteristic
414#554—738no—
415#554—1464no—
416D4×Q8—738no—
417D4×Q8—1464no—
418C2×C4⋊Q8—731no—
419C2×C4⋊Q8—731no—
420C2×C4⋊Q8—1461no—
421C2×#125—1461no—
422C2×C22⋊Q8—731no—
423C2×C22⋊Q8—731no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8—1461no—
426C2×C22⋊Q8—1461no—
427C2×C22⋊Q8—1461no—
428C2×C22⋊Q8C2×D7311yescharacteristic
429C2×C22⋊Q8C2×D7311yescharacteristic
430C2×C4×Q8—731no—
431C2×C4×Q8—731no—
432C2×C4×D4—731no—
433C2×C4×D4—1461no—
434C2×C4×D4—1461no—
435C22×C4⋊C4—731no—
436C22×C4⋊C4—731no—
437#487—738no—
438#484—738no—
439#484—738no—
440#477—738no—
441#467—738no—
442#467C2×D7318yescomplemented
443#462—738no—
444#451—738no—
445#451—738no—
446C4×Q16—738no—
447C8×D4—738no—
448C2×#107—731no—
449C2×#107—731no—
450C2×#107C2×D7311yescharacteristic
451C2×C4⋊C8—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—731no—
456C2×#103—731no—
457C2×#103—731no—
458C2×#103—738no—
459C2×#103—731no—
460C2×#103—731no—
461C2×#103—738no—
462C2×#103C2×D7311yescharacteristic
463C2×#103C2×D7311yescharacteristic
464C2×C22⋊C8—731no—
465C2×C22⋊C8—731no—
466C2×C4×C8—731no—
467C22×Q8—2922no—
468C22×Q8—2922no—
469C22×Q8—734no—
470C22×Q8—734no—
471C22×Q8—731no—
472C22×Q8—731no—
473C22×Q8—1464no—
474C22×Q8—1461no—
475C22×Q8—1461no—
476C22×Q8—1464no—
477C22×Q8—1462no—
478C22×Q8—1461no—
479C22×Q8—1462no—
480C22×Q8C22×D7311yescharacteristic
481C22×Q8C22×D7311yescharacteristic
482C22×D4—731no—
483C23×C4—731no—
484C23×C4—1461no—
485C23×C4—1461no—
486C23×C4—1461no—
487C23×C4—1461no—
488C23×C4C22×D7311yescharacteristic
489C2×Q16—42no—
490C2×Q16—2922no—
491C2×Q16—734no—
492C2×Q16—734no—
493C2×Q16—1464no—
494C2×Q16C22×D7314yes—
495C22×C8—42no—
496C22×C8—2922no—
497C22×C8—734no—
498C22×C8—731no—
499C22×C8—731no—
500C22×C8C22×D7311yescharacteristic
501C22×C8C22×D7311yescharacteristic
502C22×C8C22×D7314yes—
503C4⋊Q8—734no—
504C4⋊Q8—734no—
505C4⋊Q8—1462no—
506C4⋊Q8—1462no—
507C4⋊Q8—1468no—
508#125—1468no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—734no—
512C22⋊Q8—734no—
513C22⋊Q8—1468no—
514C22⋊Q8—1468no—
515C22⋊Q8—1468no—
516C22⋊Q8—1468no—
517C22⋊Q8—1462no—
518C22⋊Q8—1462no—
519C22⋊Q8C22×D7314yes—
520C22⋊Q8C22×D7314yes—
521C4×Q8—734no—
522C4×Q8—734no—
523C4×Q8—1462no—
524C4×Q8—1462no—
525C4×D4—734no—
526C4×D4—734no—
527C4×D4—1468no—
528C4×D4—1468no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—731no—
532C2×C4⋊C4—731no—
533C2×C4⋊C4—731no—
534C2×C4⋊C4—734no—
535C2×C4⋊C4—734no—
536C2×C4⋊C4—1462no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1461no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4—1461no—
544C2×C4⋊C4—1461no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4—1462no—
547C2×C4⋊C4C22×D7311yescharacteristic
548C2×C4⋊C4C22×D7311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—731no—
552C2×C22⋊C4—731no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4—1461no—
555C2×C42—731no—
556C2×C42—1461no—
557C2×C42—1461no—
558#107—734no—
559#107—734no—
560#107C22×D7314yes—
561C4⋊C8—734no—
562#103—734no—
563#103—734no—
564#103—734no—
565#103—734no—
566#103—734no—
567#103—734no—
568#103—734no—
569#103—734no—
570#103C22×D7314yes—
571#103C22×D7314yes—
572C22⋊C8—734no—
573C22⋊C8—734no—
574C4×C8—734no—
575C24—731no—
576C24D4×D7311yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—2928no—
584C2×Q8—2924no—
585C2×Q8—2924no—
586C2×Q8—2924no—
587C2×Q8—2924no—
588C2×Q8—2928no—
589C2×Q8—5842no—
590C2×Q8—734no—
591C2×Q8—732no—
592C2×Q8—732no—
593C2×Q8—1468no—
594C2×Q8—1464no—
595C2×Q8—1464no—
596C2×Q8—1468no—
597C2×Q8—1462no—
598C2×Q8—1462no—
599C2×Q8—1461no—
600C2×Q8—1464no—
601C2×Q8—1461no—
602C2×Q8—1462no—
603C2×Q8C23×D7312yes—
604C2×Q8C23×D7312yes—
605C2×D4—738no—
606C2×D4—734no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—2924no—
614C22×C4—2924no—
615C22×C4—5842no—
616C22×C4—5842no—
617C22×C4—731no—
618C22×C4—731no—
619C22×C4—731no—
620C22×C4—732no—
621C22×C4—732no—
622C22×C4—1464no—
623C22×C4—1464no—
624C22×C4—1464no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4—1464no—
629C22×C4—1461no—
630C22×C4—1462no—
631C22×C4—1462no—
632C22×C4D4×D7312yes—
633C22×C4D4×D7311yescharacteristic
634C22×C4C23×D7312yes—
635C22×C4C23×D7311yescharacteristic
636Q16—44no—
637Q16—2924no—
638Q16—1468no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—44no—
642C2×C8—2924no—
643C2×C8—732no—
644C2×C8—732no—
645C2×C8—1462no—
646C2×C8—1462no—
647C2×C8C23×D7312yes—
648C2×C8C23×D7312yes—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—734no—
654C4⋊C4—732no—
655C4⋊C4—732no—
656C4⋊C4—1464no—
657C4⋊C4—1464no—
658C4⋊C4—1464no—
659C4⋊C4—1464no—
660C4⋊C4—1464no—
661C4⋊C4—1464no—
662C4⋊C4—1464no—
663C4⋊C4—1464no—
664C4⋊C4—1461no—
665C4⋊C4—1464no—
666C4⋊C4—1461no—
667C4⋊C4C23×D7312yes—
668C4⋊C4C23×D7312yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—734no—
672C22⋊C4—734no—
673C22⋊C4—1464no—
674C22⋊C4—1464no—
675C42—732no—
676C42—732no—
677C42—1464no—
678C42—1464no—
679C23—22no—
680C23—22no—
681C23—732no—
682C23—734no—
683C23—1462no—
684C23—1462no—
685C23Q16×D7314yes—
686C23C2×D4×D7312yes—
687C23C2×D4×D7311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—42no—
693Q8—42no—
694Q8—2928no—
695Q8—2928no—
696Q8—2922no—
697Q8—5844no—
698Q8—734no—
699Q8—1462no—
700Q8—1462no—
701Q8—1462no—
702Q8—1464no—
703D4—7316no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—2928no—
717C2×C4—2922no—
718C2×C4—2922no—
719C2×C4—2922no—
720C2×C4—2928no—
721C2×C4—5844no—
722C2×C4—5844no—
723C2×C4—732no—
724C2×C4—734no—
725C2×C4—732no—
726C2×C4—732no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1464no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1464no—
737C2×C4C2×D4×D7312yes—
738C2×C4C2×D4×D7311yescharacteristic
739C2×C4#41×D7312yes—
740C2×C4#1455663612yes—
741C2×C4C24×D7311yescharacteristic
742C8—22no—
743C8—22no—
744C8—1462no—
745C8—1462no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—734no—
750C22—1468no—
751C22—1462no—
752C22—1462no—
753C22#1798922612yes—
754C22C2×Q16×D7314yes—
755C22C2×Q16×D7312yes—
756C22#1798939412yes—
757C22C22×D4×D7311yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—2922no—
764C4—2922no—
765C4—2922no—
766C4—734no—
767C4—1464no—
768C4—1462no—
769C4—1462no—
770C4#1798922612yes—
771C4C2×#41×D7311yescharacteristic
772C4C2×#1455663611yescharacteristic
773C2—24no—
774C2—1464no—
775C2#2262180214yesdirect product factor
776C2C2×#1798922611yescharacteristic
777C2C22×Q16×D7311yescharacteristic
778C2C2×#1798939411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#467×C73C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
hypercenterC2×#467D73
hypocenterC73C2×#3299
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #22621802C2direct (N × H)
4. C2×#17988936C2semidirect
5. C2×#17988924C2semidirect
6. C2×#17988920C2semidirect
7. C2×#17988881C2semidirect
8. C2×#17988827C2semidirect
9. C2×#17988795C2semidirect
10. C2×#17988742C2semidirect
11. C2×#17988741C2semidirect
12. C2×#17988679C2semidirect
14. C22×#14556516C2semidirect
15. C2×#103×D73C2semidirect
16. C2×#467×C73C2semidirect
43. #17988936C22semidirect
44. #17988924C22semidirect
45. #17988920C22semidirect
46. #17988881C22semidirect
47. #17988827C22semidirect
48. #17988795C22semidirect
49. #17988742C22semidirect
50. #17988741C22semidirect
51. #17988679C22semidirect
60. C2×#14556516C22semidirect
65. #103×D73C22semidirect
73. #467×C73C22semidirect
206. C2×C22⋊D73Q16semidirect
321. C22⋊D73C2×Q16semidirect
385. C2×C73#3299semidirect
398. C2×#467D73semidirect
406. C73C2×#3299semidirect
442. #467C2×D73semidirect
775. C2#22621802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892952
C2×#179892502
#226218022
C2×#179889362
C2×#179889242
C2×#179889202
C2×#179888812
C2×#179888272
C2×#179887952
C2×#179887422
C2×#179887412
C2×#179886792
C2×C8×C22⋊D732
C22×#145565162
C2×#103×D732
C2×#467×C732
C2×#329973