Finite Group Databasebeta

← C2×#22622046 #33962578

Subgroups — C2×#22622046 #33962578

Order 18688.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989295C211yesmaximal, characteristic, complemented
2C2×#17989248C211yesmaximal, characteristic
3#22622046C2116yesmaximal, direct product factor
4C2×#17988948C211yesmaximal, characteristic, complemented
5C2×#17988906C211yesmaximal, characteristic, complemented
6C2×#17988916C211yesmaximal, characteristic, complemented
7C2×#17988870C211yesmaximal, characteristic, complemented
8C2×#17988842C211yesmaximal, characteristic, complemented
9C2×#17988818C211yesmaximal, characteristic, complemented
10C2×#17988811C211yesmaximal, characteristic, complemented
11C2×#17988748C211yesmaximal, characteristic, complemented
12C2×#17988694C211yesmaximal, characteristic, complemented
13C2×#17988655C211yesmaximal, characteristic, complemented
14C2×#17988587C211yesmaximal, characteristic, complemented
15C22×#14556515C211yesmaximal, characteristic, complemented
16C2×#451×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20C23×#10596831C2211yescharacteristic
21#17989295—24no—
22#17989295C2218yescomplemented
23#17989248—24no—
24#17989248C2218yes—
25C2×#14556590C2211yescharacteristic
26C2×#14556581—21no—
27C2×#14556580—21no—
28C2×#14556580C2211yescharacteristic
29C2×#14556571—21no—
30C2×#14556568—21no—
31C2×#14556567—21no—
32C2×#14556567C2211yescharacteristic
33C2×#14556567C2211yescharacteristic
34C2×#14556565—21no—
35C2×#14556565C2211yescharacteristic
36C2×Q8×Dic73C2211yescharacteristic
37C2×Q8×Dic73C2211yescharacteristic
38C2×C4×C22⋊D73—21no—
39C2×C4×C22⋊D73C2211yescharacteristic
40C2×#14556551—21no—
41C22×C4⋊Dic73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988948C2218yescomplemented
44#17988916C2218yescomplemented
45#17988906C2218yescomplemented
46#17988870C2218yescomplemented
47#17988842C2218yescomplemented
48#17988818C2218yescomplemented
49#17988811C2218yescomplemented
50#17988748C2218yescomplemented
51#17988694C2218yescomplemented
52#17988655C2218yescomplemented
53C2×#14556523C2211yescharacteristic
54C2×#14556523C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57#17988587C2218yescomplemented
58C2×#14556515C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2218yescomplemented
64C2×#14556513C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C23×Q8×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C22×Q16×C73C2211yescharacteristic
72C2×C22⋊Q8×C73C2211yescharacteristic
73#451×C73C2218yescomplemented
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029—42no—
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×C22⋊D73—21no—
85C22×C22⋊D73D411yescharacteristic
86C23×Dic73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73C2311yescharacteristic
90C2×#11924015—42no—
91C2×#11924015C2314yes—
92C2×#11924011—42no—
93C2×#11924011C2314yes—
94C22×#10596831—42no—
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2314yes—
98#14556590—22no—
99#14556590C2314yes—
100#14556581—28no—
101#14556580—28no—
102#14556580—22no—
103#14556580C2314yes—
104#14556571—28no—
105#14556568—28no—
106#14556567—22no—
107#14556567—22no—
108#14556567—28no—
109#14556567C2314yes—
110#14556567C2314yes—
111#14556565—28no—
112#14556565—22no—
113#14556565C2314yes—
114Q8×Dic73—22no—
115Q8×Dic73—22no—
116Q8×Dic73C2314yes—
117Q8×Dic73C2314yes—
118C4×C22⋊D73—28no—
119C4×C22⋊D73D414yes—
120C4×C22⋊D73C2314yes—
121#14556551—28no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—22no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2314yes—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007D411yescharacteristic
135C4⋊C4×D73—22no—
136C4⋊C4×D73C2314yes—
137C2×C22⋊Dic73D411yescharacteristic
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005D411yescharacteristic
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556523C2314yes—
148#14556523C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556515C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556513C2314yes—
157#14556513C2314yes—
158#14556511C2314yes—
159#14556503C2314yes—
160#14556501C2314yes—
161C22×Q8×C73—22no—
162C22×Q8×C73—21no—
163C22×Q8×C73—24no—
164C22×Q8×C73—42no—
165C22×Q8×C73C2311yescharacteristic
166C22×Q8×C73C2311yescharacteristic
167C22×Q8×C73C2314yes—
168C22×Q8×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73C2311yescharacteristic
171C2×Q16×C73—24no—
172C2×Q16×C73—42no—
173C2×Q16×C73C2314yes—
174C2×Q16×C73C2314yes—
175C22×C8×C73C2311yescharacteristic
176C22×C8×C73C2311yescharacteristic
177C22⋊Q8×C73—22no—
178C22⋊Q8×C73C2314yes—
179C2×C4⋊C4×C73—21no—
180C2×C4⋊C4×C73C2311yescharacteristic
181C2×C22⋊C4×C73—21no—
182#103×C73C2314yes—
183#103×C73C2314yes—
184C22⋊C8×C73C2314yes—
185C23×D73—21no—
186C23×D73C2×D411yescharacteristic
187#11924029—28no—
188#11924029—44no—
189#11924029—48no—
190C2×Dic146—24no—
191C2×Dic146—82no—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—24no—
195C2×D292—21no—
196C2×D292—44no—
197C2×D292C2412yes—
198C2×C22⋊D73—24no—
199C2×C22⋊D73—24no—
200C2×C22⋊D73—44no—
201C2×C22⋊D73C2×D414yes—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—24no—
206C22×Dic73—82no—
207C22×Dic73C2×D411yescharacteristic
208C22×Dic73C2×D411yescharacteristic
209C22×Dic73C2×D411yescharacteristic
210C2×C4×D73—22no—
211C2×C4×D73—22no—
212C2×C4×D73—24no—
213C2×C4×D73—24no—
214C2×C4×D73—44no—
215C2×C4×D73—82no—
216C2×C4×D73C2×D412yes—
217C2×C4×D73C2412yes—
218#11924015—44no—
219#11924011—44no—
220C2×#10596831—22no—
221C2×#10596831—22no—
222C2×#10596831—44no—
223C2×#10596831C2412yes—
224C2×#10596831C2412yes—
225C4⋊Dic73—21no—
226C4⋊Dic73—21no—
227C4⋊Dic73—24no—
228C4⋊Dic73—21no—
229C4⋊Dic73—24no—
230C4⋊Dic73—24no—
231C4⋊Dic73C2412yes—
232C4⋊Dic73C2412yes—
233C4⋊Dic73C2412yes—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924007—24no—
238#11924007C2×D414yes—
239C22⋊Dic73C2×D414yes—
240#11924005—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005—24no—
245#11924005C2×D414yes—
246C4×Dic73—24no—
247C4×Dic73—24no—
248C4×Dic73C2×D412yes—
249C4×Dic73C2412yes—
250C24×C73C2×D411yescharacteristic
251C2×Q8×C73—21no—
252C2×Q8×C73—21no—
253C2×Q8×C73—24no—
254C2×Q8×C73—21no—
255C2×Q8×C73—22no—
256C2×Q8×C73—28no—
257C2×Q8×C73—22no—
258C2×Q8×C73—22no—
259C2×Q8×C73—22no—
260C2×Q8×C73—22no—
261C2×Q8×C73—44no—
262C2×Q8×C73—44no—
263C2×Q8×C73—48no—
264C2×Q8×C73#4114yes—
265C2×Q8×C73C2412yes—
266C2×Q8×C73C2412yes—
267C2×Q8×C73C2412yes—
268C22×C4×C73—21no—
269C22×C4×C73—22no—
270C22×C4×C73—22no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—24no—
275C22×C4×C73—44no—
276C22×C4×C73C2×D411yescharacteristic
277C22×C4×C73C2×D412yes—
278C22×C4×C73C2412yes—
279C22×C4×C73C2411yescharacteristic
280Q16×C73—28no—
281Q16×C73—44no—
282C2×C8×C73—22no—
283C2×C8×C73—22no—
284C2×C8×C73C2412yes—
285C2×C8×C73C2412yes—
286C4⋊C4×C73—24no—
287C4⋊C4×C73—21no—
288C4⋊C4×C73C2412yes—
289C22⋊C4×C73—24no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73#13714yes—
293C23×C73C22×D412yes—
294C23×C73C22×D411yescharacteristic
295C22×D73—22no—
296C22×D73—22no—
297C22×D73—22no—
298C22×D73—22no—
299C22×D73—42no—
300C22×D73—42no—
301C22×D73—42no—
302C22×D73C22×D412yes—
303Q8×C73—24no—
304Q8×C73—22no—
305Q8×C73—22no—
306Q8×C73—22no—
307Q8×C73—22no—
308Q8×C73—22no—
309Q8×C73—48no—
310Q8×C73—42no—
311Q8×C73—42no—
312Q8×C73C2×#4114yes—
313C2×C4×C73—22no—
314C2×C4×C73—24no—
315C2×C4×C73—22no—
316C2×C4×C73—24no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—48no—
323C2×C4×C73—42no—
324C2×C4×C73—42no—
325C2×C4×C73—42no—
326C2×C4×C73C22×D412yes—
327C2×C4×C73C22×D411yescharacteristic
328C2×C4×C73C2×#4112yes—
329C2×C4×C73H(5,𝔽2)12yes—
330C2×C4×C73C2511yescharacteristic
331C22⋊D73—28no—
332C22⋊D73—48no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—42no—
340C2×Dic73—42no—
341C2×Dic73—42no—
342C2×Dic73—84no—
343C2×Dic73C22×D412yes—
344C2×Dic73C22×D412yes—
345C2×Dic73C22×D412yes—
346D292—22no—
347D292—22no—
348D292—48no—
349D292—42no—
350C4×D73—24no—
351C4×D73—22no—
352C4×D73—22no—
353C4×D73—48no—
354C4×D73—84no—
355Dic146—84no—
356C8×C73—22no—
357C8×C73—22no—
358#10596831—22no—
359#10596831—22no—
360C22×C73—22no—
361C22×C73—28no—
362C22×C73—22no—
363C22×C73#54612yes—
364C22×C73C2×#13714yes—
365C22×C73C2×#13712yes—
366C22×C73#57712yes—
367C22×C73C23×D411yescharacteristic
368C2×D73—22no—
369C2×D73—22no—
370C2×D73—22no—
371C2×D73—44no—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—42no—
375C2×D73—84no—
376C4×C73—24no—
377C4×C73—22no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73—42no—
381C4×C73#54612yes—
382C4×C73C22×#4111yescharacteristic
383C4×C73C2×H(5,𝔽2)11yescharacteristic
384Dic73—22no—
385Dic73—22no—
386Dic73—22no—
387Dic73—42no—
388Dic73—42no—
389Dic73—42no—
390C2×#3316—731nomaximal, Sylow
391C2×C73—24no—
392C2×C73#331614yescomplemented
393C2×C73C2×#54611yescharacteristic
394C2×C73C22×#13711yescharacteristic
395C2×C73C2×#57711yescharacteristic
396D73—42no—
397D73—82no—
398C2×#554—731no—
399C2×#548—731no—
400#3316—7316no—
401C2×#489—731no—
402C2×#481—731no—
403C2×#483—731no—
404C2×#475—731no—
405C2×#470—731no—
406C2×#465—731no—
407C2×#464—731no—
408C2×#452—731no—
409C2×#451D7311yescharacteristic, complemented
410C2×#441—731no—
411C2×#435—731no—
412C2×#417—731no—
413C22×#103—731no—
414C73C2×#331611yescharacteristic, complemented, Sylow
415C22×#41—731no—
416C23×Q8C2×D7311yescharacteristic
417C22×Q16C2×D7311yescharacteristic
418C22×Q16C2×D7311yescharacteristic
419C22×SD16—731no—
420C22×M16—731no—
421C23×C8—731no—
422#554—738no—
423#554—1464no—
424#548—738no—
425#548—1464no—
426C2×C4⋊Q8—731no—
427C2×#125—1461no—
428C2×#124—731no—
429C2×#124—1461no—
430C2×C22⋊Q8—731no—
431C2×C22⋊Q8—731no—
432C2×C22⋊Q8—1461no—
433C2×C22⋊Q8—1461no—
434C2×C22⋊Q8—1461no—
435C2×C22⋊Q8C2×D7311yescharacteristic
436C2×#121—731no—
437C2×#121—1461no—
438C2×C4×Q8—731no—
439C2×C4×Q8—731no—
440C2×C4×D4—731no—
441C2×C4×D4—1461no—
442C2×C4×D4—1461no—
443C22×C4⋊C4—731no—
444C22×C4⋊C4—731no—
445#489—738no—
446#483—738no—
447#481—738no—
448#475—738no—
449#470—738no—
450#465—738no—
451#464—738no—
452#452—738no—
453#451C2×D7318yescomplemented
454#441—738no—
455#435—738no—
456C2×#106—731no—
457C2×#106—731no—
458C2×#106—731no—
459C2×C4⋊C8—731no—
460#417—738no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#103—738no—
466C2×#103—731no—
467C2×#103C2×D7311yescharacteristic
468C2×#103C2×D7311yescharacteristic
469C2×#102—731no—
470C2×#102—731no—
471C2×#102—731no—
472C2×C22⋊C8—731no—
473C2×C22⋊C8C2×D7311yescharacteristic
474C2×#97—731no—
475C2×#41—2922no—
476C2×#41—734no—
477C2×#41—1464no—
478C2×#41—1462no—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—24no—
482C22×Q8—42no—
483C22×Q8—1461no—
484C22×Q8C22×D7311yescharacteristic
485C22×Q8C22×D7311yescharacteristic
486C22×Q8C22×D7314yes—
487C22×Q8C22×D7311yescharacteristic
488C22×D4—731no—
489C22×D4—731no—
490C22×D4—1461no—
491C22×D4—1461no—
492C23×C4—21no—
493C23×C4—731no—
494C23×C4—1461no—
495C23×C4—1461no—
496C23×C4—1461no—
497C23×C4C22×D7311yescharacteristic
498C2×Q16—24no—
499C2×Q16—42no—
500C2×Q16C22×D7314yes—
501C2×Q16C22×D7314yes—
502C2×SD16—2922no—
503C2×SD16—734no—
504C2×M16—2922no—
505C2×M16—734no—
506C22×C8—2922no—
507C22×C8—734no—
508C22×C8—731no—
509C22×C8—731no—
510C22×C8C22×D7311yescharacteristic
511C22×C8C22×D7311yescharacteristic
512C4⋊Q8—734no—
513C4⋊Q8—1462no—
514#125—1468no—
515#124—734no—
516#124—1462no—
517#124—1468no—
518C22⋊Q8—22no—
519C22⋊Q8—734no—
520C22⋊Q8—734no—
521C22⋊Q8—1468no—
522C22⋊Q8—1468no—
523C22⋊Q8—1468no—
524C22⋊Q8—1462no—
525C22⋊Q8—1462no—
526C22⋊Q8C22×D7314yes—
527#121—734no—
528#121—1468no—
529#121—1462no—
530C4×Q8—734no—
531C4×Q8—734no—
532C4×Q8—1462no—
533C4×Q8—1462no—
534C4×D4—734no—
535C4×D4—734no—
536C4×D4—1468no—
537C4×D4—1468no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—731no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—731no—
542C2×C4⋊C4—734no—
543C2×C4⋊C4—731no—
544C2×C4⋊C4—734no—
545C2×C4⋊C4—1462no—
546C2×C4⋊C4—1461no—
547C2×C4⋊C4—1461no—
548C2×C4⋊C4—1461no—
549C2×C4⋊C4—1461no—
550C2×C4⋊C4—1461no—
551C2×C4⋊C4—1461no—
552C2×C4⋊C4—1461no—
553C2×C4⋊C4—1462no—
554C2×C4⋊C4C22×D7311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—731no—
557C2×C22⋊C4—731no—
558C2×C22⋊C4—1461no—
559C2×C22⋊C4—1461no—
560C2×C22⋊C4—1461no—
561C2×C22⋊C4—1461no—
562C2×C22⋊C4—1461no—
563C2×C42—731no—
564C2×C42—1461no—
565C2×C42—1461no—
566#106—734no—
567#106—734no—
568#106—734no—
569C4⋊C8—734no—
570#103—734no—
571#103—734no—
572#103—734no—
573#103—734no—
574#103—734no—
575#103C22×D7314yes—
576#103C22×D7314yes—
577#102—734no—
578#102—734no—
579#102—734no—
580C22⋊C8—734no—
581C22⋊C8C22×D7314yes—
582#97—734no—
583C24—731no—
584C24—1461no—
585C24D4×D7311yescharacteristic
586#41—2928no—
587#41—2924no—
588#41—1468no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—24no—
592C2×Q8—21no—
593C2×Q8—22no—
594C2×Q8—28no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—48no—
602C2×Q8—5842no—
603C2×Q8—1464no—
604C2×Q8#1192402714yes—
605C2×Q8C23×D7312yes—
606C2×Q8C23×D7312yes—
607C2×Q8C23×D7312yes—
608C2×D4—2924no—
609C2×D4—2924no—
610C2×D4—734no—
611C2×D4—732no—
612C2×D4—1464no—
613C2×D4—1464no—
614C2×D4—1464no—
615C2×D4—1461no—
616C2×D4—1462no—
617C2×D4—1462no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—44no—
626C22×C4—2924no—
627C22×C4—5842no—
628C22×C4—5842no—
629C22×C4—731no—
630C22×C4—731no—
631C22×C4—731no—
632C22×C4—732no—
633C22×C4—732no—
634C22×C4—1464no—
635C22×C4—1464no—
636C22×C4—1461no—
637C22×C4—1461no—
638C22×C4—1461no—
639C22×C4—1464no—
640C22×C4—1462no—
641C22×C4—1462no—
642C22×C4D4×D7312yes—
643C22×C4D4×D7311yescharacteristic
644C22×C4C23×D7312yes—
645C22×C4C23×D7311yescharacteristic
646Q16—28no—
647Q16—44no—
648SD16—2924no—
649M16—2924no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—2924no—
653C2×C8—732no—
654C2×C8—732no—
655C2×C8—1462no—
656C2×C8—1462no—
657C2×C8C23×D7312yes—
658C2×C8C23×D7312yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—734no—
662C4⋊C4—732no—
663C4⋊C4—732no—
664C4⋊C4—732no—
665C4⋊C4—1464no—
666C4⋊C4—1464no—
667C4⋊C4—1464no—
668C4⋊C4—1464no—
669C4⋊C4—1464no—
670C4⋊C4—1464no—
671C4⋊C4—1461no—
672C4⋊C4—1464no—
673C4⋊C4—1461no—
674C4⋊C4—1461no—
675C4⋊C4C23×D7312yes—
676C22⋊C4—24no—
677C22⋊C4—734no—
678C22⋊C4—734no—
679C22⋊C4—1464no—
680C22⋊C4—1464no—
681C22⋊C4—1464no—
682C22⋊C4—1464no—
683C22⋊C4—1464no—
684C42—732no—
685C42—732no—
686C42—1464no—
687C42—1464no—
688C23—22no—
689C23—22no—
690C23—2922no—
691C23—2922no—
692C23—2922no—
693C23—732no—
694C23—1462no—
695C23—1462no—
696C23—1462no—
697C23—1462no—
698C23#1455662314yes—
699C23C2×D4×D7312yes—
700C23C2×D4×D7311yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—48no—
708Q8—42no—
709Q8—42no—
710Q8—5844no—
711Q8C2×#1192402714yes—
712D4—2928no—
713D4—2928no—
714D4—2922no—
715D4—1468no—
716D4—1462no—
717D4—1462no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—2928no—
732C2×C4—2922no—
733C2×C4—2922no—
734C2×C4—2922no—
735C2×C4—5844no—
736C2×C4—5844no—
737C2×C4—732no—
738C2×C4—732no—
739C2×C4—732no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1462no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4—1464no—
749C2×C4C2×D4×D7312yes—
750C2×C4C2×D4×D7311yescharacteristic
751C2×C4C2×#1192402712yes—
752C2×C4#1455663612yes—
753C2×C4C24×D7311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1462no—
757C8—1462no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—2924no—
762C22—2922no—
763C22—2922no—
764C22—2922no—
765C22—5844no—
766C22—1462no—
767C22—1462no—
768C22—1462no—
769C22#1798922412yes—
770C22C2×#1455662314yes—
771C22C2×#1455662312yes—
772C22#1798939612yes—
773C22C22×D4×D7311yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—2922no—
780C4—2922no—
781C4—2922no—
782C4—1462no—
783C4—1462no—
784C4—1462no—
785C4#1798922412yes—
786C4C22×#1192402711yescharacteristic
787C4C2×#1455663611yescharacteristic
788C2—24no—
789C2—2922no—
790C2—5842no—
791C2#2262204614yesdirect product factor
792C2C2×#1798922411yescharacteristic
793C2C22×#1455662311yescharacteristic
794C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#451×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989248C2
hypercenterC2×#451D73
hypocenterC73C2×#3316
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#17989295C2semidirect
3. #22622046C2direct (N × H)
4. C2×#17988948C2semidirect
5. C2×#17988906C2semidirect
6. C2×#17988916C2semidirect
7. C2×#17988870C2semidirect
8. C2×#17988842C2semidirect
9. C2×#17988818C2semidirect
10. C2×#17988811C2semidirect
11. C2×#17988748C2semidirect
12. C2×#17988694C2semidirect
13. C2×#17988655C2semidirect
14. C2×#17988587C2semidirect
15. C22×#14556515C2semidirect
16. C2×#451×C73C2semidirect
22. #17989295C22semidirect
43. #17988948C22semidirect
44. #17988916C22semidirect
45. #17988906C22semidirect
46. #17988870C22semidirect
47. #17988842C22semidirect
48. #17988818C22semidirect
49. #17988811C22semidirect
50. #17988748C22semidirect
51. #17988694C22semidirect
52. #17988655C22semidirect
57. #17988587C22semidirect
63. C2×#14556515C22semidirect
73. #451×C73C22semidirect
392. C2×C73#3316semidirect
409. C2×#451D73semidirect
414. C73C2×#3316semidirect
453. #451C2×D73semidirect
791. C2#22622046direct (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×#179892482
#226220462
C2×#179889482
C2×#179889062
C2×#179889162
C2×#179888702
C2×#179888422
C2×#179888182
C2×#179888112
C2×#179887482
C2×#179886942
C2×#179886552
C2×#179885872
C22×#145565152
C2×#451×C732
C2×#331673