Finite Group Databasebeta

← C2×#22622223 #33962879

Subgroups — C2×#22622223 #33962879

Order 18688.

2146 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×#17989300C211yesmaximal, characteristic
2C2×#17989250C211yesmaximal, characteristic, complemented
3#22622223C2116yesmaximal, direct product factor
4C2×#17988936C211yesmaximal, characteristic, complemented
5C2×#17988931C211yesmaximal, characteristic, complemented
6C2×#17988881C211yesmaximal, characteristic, complemented
7C2×#17988835C211yesmaximal, characteristic, complemented
8C2×#17988834C211yesmaximal, characteristic, complemented
9C2×#17988791C211yesmaximal, characteristic, complemented
10C2×#17988728C211yesmaximal, characteristic, complemented
11C2×#17988727C211yesmaximal, characteristic, complemented
12C2×#17988674C211yesmaximal, characteristic, complemented
13C2×#17988662C211yesmaximal, characteristic, complemented
14C2×#17988595C211yesmaximal, characteristic, complemented
15C2×#17988594C211yesmaximal, characteristic, complemented
16C2×#485×C73C211yesmaximal, characteristic, complemented
17C23×Dic146C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22C22×#11924012C2211yescharacteristic
23C22×#11924011C2211yescharacteristic
24#17989300—24no—
25#17989300C2218yes—
26#17989250—24no—
27#17989250C2218yescomplemented
28C2×#14556590—21no—
29C2×#14556590C2211yescharacteristic
30C2×#14556589C2211yescharacteristic
31C2×#14556579—21no—
32C2×#14556577—21no—
33C2×#14556571C2211yescharacteristic
34C2×#14556569—21no—
35C2×#14556568—21no—
36C2×#14556566C2211yescharacteristic
37C2×#14556565C2211yescharacteristic
38C2×#14556564—21no—
39C2×#14556556C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×C4×C22⋊D73C2211yescharacteristic
42C2×#14556551—21no—
43C2×#14556549C2211yescharacteristic
44C2×#14556548—21no—
45#17988936C2218yescomplemented
46#17988931C2218yescomplemented
47#17988881C2218yescomplemented
48#17988835C2218yescomplemented
49#17988834C2218yescomplemented
50#17988791C2218yescomplemented
51#17988728C2218yescomplemented
52#17988727C2218yescomplemented
53#17988674C2218yescomplemented
54#17988662C2218yescomplemented
55C2×#14556524C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57#17988595C2218yescomplemented
58#17988594C2218yescomplemented
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C22⋊Q8×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71#485×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C22⋊C8×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×D292—21no—
91C22×D292C2311yescharacteristic
92C22×C22⋊D73—21no—
93C22×C22⋊D73D411yescharacteristic
94C23×Dic73—21no—
95C22×C4×D73—21no—
96C22×C4×D73—21no—
97C22×C4×D73C2311yescharacteristic
98C2×#11924017—24no—
99C2×#11924017—42no—
100C2×#11924017C2314yes—
101C2×#11924017C2314yes—
102C2×#11924015—42no—
103C2×#11924015C2314yes—
104C2×#11924012—42no—
105C2×#11924012C2314yes—
106C2×#11924011—42no—
107C2×#11924011C2314yes—
108C22×#10596831C2311yescharacteristic
109C22×#10596831C2311yescharacteristic
110#14556590—28no—
111#14556590—22no—
112#14556590C2314yes—
113#14556589—22no—
114#14556589C2314yes—
115#14556579—28no—
116#14556577—28no—
117#14556571—22no—
118#14556571C2314yes—
119#14556569—28no—
120#14556568—28no—
121#14556566—22no—
122#14556566C2314yes—
123#14556565—22no—
124#14556565C2314yes—
125#14556564—28no—
126#14556556—22no—
127#14556556C2314yes—
128#14556553—22no—
129#14556553C2314yes—
130C4×C22⋊D73D414yes—
131C4×C22⋊D73C2314yes—
132#14556551—28no—
133#14556549—22no—
134#14556549C2314yes—
135#14556548—28no—
136C2×C4⋊Dic73—21no—
137C2×C4⋊Dic73C2311yescharacteristic
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×#11924007—21no—
142C2×#11924007D411yescharacteristic
143C2×C22⋊Dic73D411yescharacteristic
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×#11924005D411yescharacteristic
150C2×C4×Dic73—21no—
151C2×C4×Dic73—21no—
152C2×C4×Dic73C2311yescharacteristic
153#14556524C2314yes—
154#14556520C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556515C2314yes—
158#14556514C2314yes—
159#14556514C2314yes—
160#14556514C2314yes—
161#14556514C2314yes—
162#14556511C2314yes—
163#14556503C2314yes—
164C8×Dic73C2314yes—
165C22×Q8×C73C2311yescharacteristic
166C23×C4×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C22⋊Q8×C73—22no—
170C22⋊Q8×C73C2314yes—
171#117×C73—22no—
172#117×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C42×C73—21no—
180#107×C73C2314yes—
181#106×C73C2314yes—
182#103×C73C2314yes—
183#103×C73C2314yes—
184C22⋊C8×C73C2314yes—
185C23×D73—21no—
186C23×D73C2×D411yescharacteristic
187C2×Dic146—21no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—28no—
192C2×Dic146—24no—
193C2×Dic146—21no—
194C2×Dic146—24no—
195C2×Dic146—24no—
196C2×Dic146—44no—
197C2×Dic146—48no—
198C2×Dic146—44no—
199C2×Dic146—44no—
200C2×Dic146—82no—
201C2×Dic146#4114yes—
202C2×Dic146C2412yes—
203C2×Dic146C2412yes—
204Q8×D73—28no—
205Q8×D73—44no—
206Q8×D73—48no—
207C2×D292—22no—
208C2×D292—22no—
209C2×D292—21no—
210C2×D292—24no—
211C2×D292—82no—
212C2×D292C2412yes—
213C2×C22⋊D73—24no—
214C2×C22⋊D73—24no—
215C2×C22⋊D73—82no—
216C2×C22⋊D73C2×D414yes—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C22×Dic73—21no—
220C22×Dic73—24no—
221C22×Dic73—44no—
222C22×Dic73C2×D411yescharacteristic
223C22×Dic73C2×D411yescharacteristic
224C22×Dic73C2×D411yescharacteristic
225C2×C4×D73—22no—
226C2×C4×D73—22no—
227C2×C4×D73—24no—
228C2×C4×D73—24no—
229C2×C4×D73—44no—
230C2×C4×D73—44no—
231C2×C4×D73C2×D412yes—
232C2×C4×D73C2412yes—
233#11924017—28no—
234#11924017—44no—
235#11924015—44no—
236#11924012—44no—
237#11924011—44no—
238C2×#10596831—22no—
239C2×#10596831—22no—
240C2×#10596831C2412yes—
241C2×#10596831C2412yes—
242C4⋊Dic73—21no—
243C4⋊Dic73—24no—
244C4⋊Dic73C2412yes—
245#11924007—24no—
246#11924007—24no—
247#11924007—24no—
248#11924007—24no—
249#11924007C2×D414yes—
250C22⋊Dic73C2×D414yes—
251#11924005—24no—
252#11924005—24no—
253#11924005—24no—
254#11924005—24no—
255#11924005—24no—
256#11924005C2×D414yes—
257C4×Dic73—24no—
258C4×Dic73—24no—
259C4×Dic73C2×D412yes—
260C4×Dic73C2412yes—
261C24×C73C2×D411yescharacteristic
262C2×Q8×C73—21no—
263C2×Q8×C73—22no—
264C2×Q8×C73—22no—
265C2×Q8×C73C2412yes—
266C22×C4×C73—22no—
267C22×C4×C73—22no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73C2×D411yescharacteristic
273C22×C4×C73C2×D412yes—
274C22×C4×C73C2412yes—
275C22×C4×C73C2411yescharacteristic
276C2×C8×C73—22no—
277C2×C8×C73—22no—
278C2×C8×C73C2412yes—
279C2×C8×C73C2412yes—
280C4⋊C4×C73—24no—
281C4⋊C4×C73—21no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73C2412yes—
285C4⋊C4×C73C2412yes—
286C4⋊C4×C73C2412yes—
287C22⋊C4×C73—24no—
288C22⋊C4×C73—24no—
289C42×C73—24no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
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—22no—
304Q8×C73—22no—
305Q8×C73—42no—
306C2×C4×C73—22no—
307C2×C4×C73—24no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73—42no—
318C2×C4×C73C22×D412yes—
319C2×C4×C73C22×D411yescharacteristic
320C2×C4×C73C2×#4112yes—
321C2×C4×C73H(5,𝔽2)12yes—
322C2×C4×C73C2511yescharacteristic
323C22⋊D73—28no—
324C22⋊D73—84no—
325C2×Dic73—22no—
326C2×Dic73—24no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—48no—
332C2×Dic73—42no—
333C2×Dic73—42no—
334C2×Dic73#13714yes—
335C2×Dic73C22×D412yes—
336C2×Dic73C22×D412yes—
337C2×Dic73C22×D412yes—
338D292—22no—
339D292—22no—
340D292—42no—
341D292—84no—
342C4×D73—24no—
343C4×D73—22no—
344C4×D73—22no—
345C4×D73—48no—
346C4×D73—48no—
347Dic146—24no—
348Dic146—22no—
349Dic146—22no—
350Dic146—22no—
351Dic146—48no—
352Dic146—48no—
353Dic146—42no—
354Dic146—84no—
355Dic146C2×#4114yes—
356C8×C73—22no—
357C8×C73—22no—
358#10596831—22no—
359#10596831—22no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—22no—
363C22×C73—44no—
364C22×C73#54612yes—
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—22no—
377C4×C73—42no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73—42no—
381C4×C73#54612yes—
382C4×C73C22×#4111yescharacteristic
383C4×C73C2×H(5,𝔽2)11yescharacteristic
384Dic73—24no—
385Dic73—22no—
386Dic73—22no—
387Dic73—42no—
388Dic73—42no—
389Dic73C2×#13714yes—
390C2×#3329—731nomaximal, Sylow
391C2×C73—42no—
392C2×C73#332914yescomplemented
393C2×C73C2×#54611yescharacteristic
394C2×C73C22×#13711yescharacteristic
395C2×C73C2×#57711yescharacteristic
396D73—42no—
397D73—82no—
398C2×#555—731no—
399C2×D4×Q8—731no—
400#3329—7316no—
401C2×#487—731no—
402C2×#485—731no—
403C2×#485D7311yescharacteristic, complemented
404C2×#477—731no—
405C2×#468—731no—
406C2×#468—731no—
407C2×#461—731no—
408C2×#448—731no—
409C2×#448—731no—
410C2×C4×SD16—731no—
411C2×#436—731no—
412C2×#419—731no—
413C2×#419—731no—
414C73C2×#332911yescharacteristic, complemented, Sylow
415C23×Q8—731no—
416C23×Q8—731no—
417C22×SD16—731no—
418C22×SD16—731no—
419C22×SD16—731no—
420C22×M16—731no—
421C22×M16—731no—
422#555—738no—
423#555—1464no—
424D4×Q8—738no—
425D4×Q8—1464no—
426C2×C4⋊Q8—731no—
427C2×C4⋊Q8—731no—
428C2×C4⋊Q8—1461no—
429C2×#124—1461no—
430C2×#124—1461no—
431C2×C22⋊Q8—731no—
432C2×C22⋊Q8—1461no—
433C2×C22⋊Q8—1461no—
434C2×C22⋊Q8C2×D7311yescharacteristic
435C2×#121—731no—
436C2×#121—731no—
437C2×#121—1461no—
438C2×C4×Q8—731no—
439C2×C4×D4—731no—
440C2×C4×D4—731no—
441C2×C4×D4—1461no—
442C2×#117—731no—
443C2×#117—1461no—
444C2×#117C2×D7311yescharacteristic
445#487—738no—
446#485—738no—
447#485C2×D7318yescomplemented
448#477—738no—
449#468—738no—
450#468—738no—
451#461—738no—
452#448—738no—
453#448—738no—
454C4×SD16—738no—
455#436—738no—
456C2×#107—731no—
457C2×#107C2×D7311yescharacteristic
458C2×#106C2×D7311yescharacteristic
459C2×C4⋊C8—731no—
460#419—738no—
461#419—738no—
462C2×#103—731no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#103—731no—
466C2×#103—731no—
467C2×#103—731no—
468C2×#103—731no—
469C2×#103C2×D7311yescharacteristic
470C2×#103C2×D7311yescharacteristic
471C2×#102—731no—
472C2×C22⋊C8—731no—
473C2×C22⋊C8C2×D7311yescharacteristic
474C2×C4×C8—731no—
475C22×Q8—2922no—
476C22×Q8—2922no—
477C22×Q8—734no—
478C22×Q8—734no—
479C22×Q8—731no—
480C22×Q8—731no—
481C22×Q8—1464no—
482C22×Q8—1461no—
483C22×Q8—1461no—
484C22×Q8—1464no—
485C22×Q8—1462no—
486C22×Q8—1461no—
487C22×Q8—1462no—
488C22×Q8C22×D7311yescharacteristic
489C22×D4—731no—
490C22×D4—731no—
491C22×D4—1461no—
492C22×D4—1461no—
493C23×C4—731no—
494C23×C4—1461no—
495C23×C4—1461no—
496C23×C4—1461no—
497C23×C4C22×D7311yescharacteristic
498C2×SD16—2922no—
499C2×SD16—2922no—
500C2×SD16—734no—
501C2×SD16—734no—
502C2×SD16—734no—
503C2×SD16—1464no—
504C2×M16—2922no—
505C2×M16—2922no—
506C2×M16—734no—
507C2×M16—734no—
508C22×C8—731no—
509C22×C8—731no—
510C22×C8C22×D7311yescharacteristic
511C22×C8C22×D7311yescharacteristic
512C4⋊Q8—734no—
513C4⋊Q8—734no—
514C4⋊Q8—1462no—
515C4⋊Q8—1462no—
516C4⋊Q8—1468no—
517#124—1468no—
518#124—1468no—
519C22⋊Q8—22no—
520C22⋊Q8—734no—
521C22⋊Q8—1468no—
522C22⋊Q8—1468no—
523C22⋊Q8—1462no—
524C22⋊Q8C22×D7314yes—
525#121—734no—
526#121—734no—
527#121—1468no—
528#121—1462no—
529#121—1462no—
530C4×Q8—734no—
531C4×Q8—1462no—
532C4×D4—734no—
533C4×D4—734no—
534C4×D4—734no—
535C4×D4—1462no—
536C4×D4—1468no—
537#117—22no—
538#117—734no—
539#117—1468no—
540#117—1462no—
541#117C22×D7314yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—731no—
544C2×C4⋊C4—731no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4—1461no—
547C2×C4⋊C4—1461no—
548C2×C4⋊C4—1461no—
549C2×C4⋊C4—1461no—
550C2×C4⋊C4C22×D7311yescharacteristic
551C2×C4⋊C4C22×D7311yescharacteristic
552C2×C4⋊C4C22×D7311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—731no—
556C2×C22⋊C4—731no—
557C2×C22⋊C4—1461no—
558C2×C22⋊C4—1461no—
559C2×C22⋊C4—1461no—
560C2×C22⋊C4—1461no—
561C2×C22⋊C4—1461no—
562C2×C42—21no—
563C2×C42—731no—
564C2×C42—1461no—
565C2×C42—1461no—
566#107—734no—
567#107C22×D7314yes—
568#106C22×D7314yes—
569C4⋊C8—734no—
570#103—734no—
571#103—734no—
572#103—734no—
573#103—734no—
574#103—734no—
575#103—734no—
576#103—734no—
577#103C22×D7314yes—
578#103C22×D7314yes—
579#102—734no—
580C22⋊C8—734no—
581C22⋊C8C22×D7314yes—
582C4×C8—734no—
583C24—731no—
584C24—1461no—
585C24D4×D7311yescharacteristic
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—2928no—
590C2×Q8—2924no—
591C2×Q8—2924no—
592C2×Q8—2924no—
593C2×Q8—2924no—
594C2×Q8—2928no—
595C2×Q8—5842no—
596C2×Q8—734no—
597C2×Q8—732no—
598C2×Q8—732no—
599C2×Q8—1468no—
600C2×Q8—1464no—
601C2×Q8—1464no—
602C2×Q8—1468no—
603C2×Q8—1462no—
604C2×Q8—1462no—
605C2×Q8—1461no—
606C2×Q8—1464no—
607C2×Q8—1461no—
608C2×Q8—1462no—
609C2×Q8C23×D7312yes—
610C2×D4—5842no—
611C2×D4—5842no—
612C2×D4—734no—
613C2×D4—732no—
614C2×D4—1464no—
615C2×D4—1464no—
616C2×D4—1464no—
617C2×D4—1461no—
618C2×D4—1462no—
619C2×D4—1462no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—2924no—
627C22×C4—2924no—
628C22×C4—2924no—
629C22×C4—731no—
630C22×C4—731no—
631C22×C4—731no—
632C22×C4—732no—
633C22×C4—732no—
634C22×C4—1464no—
635C22×C4—1464no—
636C22×C4—1464no—
637C22×C4—1461no—
638C22×C4—1461no—
639C22×C4—1461no—
640C22×C4—1462no—
641C22×C4—1462no—
642C22×C4D4×D7312yes—
643C22×C4D4×D7311yescharacteristic
644C22×C4C23×D7312yes—
645C22×C4C23×D7311yescharacteristic
646SD16—2924no—
647SD16—2924no—
648SD16—1468no—
649M16—2924no—
650M16—2924no—
651C2×C8—22no—
652C2×C8—22no—
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—21no—
662C4⋊C4—21no—
663C4⋊C4—734no—
664C4⋊C4—732no—
665C4⋊C4—1464no—
666C4⋊C4—1464no—
667C4⋊C4—1464no—
668C4⋊C4—1464no—
669C4⋊C4—1464no—
670C4⋊C4—1461no—
671C4⋊C4C23×D7312yes—
672C4⋊C4C23×D7312yes—
673C4⋊C4C23×D7312yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—734no—
677C22⋊C4—734no—
678C22⋊C4—1464no—
679C22⋊C4—1464no—
680C22⋊C4—1464no—
681C22⋊C4—1464no—
682C22⋊C4—1464no—
683C42—24no—
684C42—732no—
685C42—732no—
686C42—1464no—
687C42—1464no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—2922no—
692C23—2922no—
693C23—2922no—
694C23—732no—
695C23—1462no—
696C23—1462no—
697C23—1462no—
698C23—1462no—
699C23C2×D4×D7312yes—
700C23C2×D4×D7311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—2928no—
705Q8—2928no—
706Q8—2922no—
707Q8—5844no—
708Q8—734no—
709Q8—1462no—
710Q8—1462no—
711Q8—1462no—
712Q8—1464no—
713D4—2922no—
714D4—5844no—
715D4—5844no—
716D4—1468no—
717D4—1462no—
718D4—1462no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—2928no—
732C2×C4—2928no—
733C2×C4—2922no—
734C2×C4—2922no—
735C2×C4—2928no—
736C2×C4—734no—
737C2×C4—732no—
738C2×C4—732no—
739C2×C4—732no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1464no—
745C2×C4—1462no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4—1464no—
749C2×C4C2×D4×D7312yes—
750C2×C4C2×D4×D7311yescharacteristic
751C2×C4#41×D7312yes—
752C2×C4#1455663712yes—
753C2×C4C24×D7311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1462no—
757C8—1462no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—2924no—
763C22—2922no—
764C22—2922no—
765C22—2922no—
766C22—5844no—
767C22—1462no—
768C22—1462no—
769C22—1462no—
770C22#1798922912yes—
771C22#137×D7312yes—
772C22#1798939412yes—
773C22C22×D4×D7311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—2922no—
780C4—2922no—
781C4—734no—
782C4—1464no—
783C4—1462no—
784C4—1462no—
785C4#1798922912yes—
786C4C2×#41×D7311yescharacteristic
787C4C2×#1455663711yescharacteristic
788C2—42no—
789C2—2922no—
790C2—5842no—
791C2#2262222314yesdirect product factor
792C2C2×#1798922911yescharacteristic
793C2C2×#137×D7311yescharacteristic
794C2C2×#1798939411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#485×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989300C2
hypercenterC2×#485D73
hypocenterC73C2×#3329
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#17989250C2semidirect
3. #22622223C2direct (N × H)
4. C2×#17988936C2semidirect
5. C2×#17988931C2semidirect
6. C2×#17988881C2semidirect
7. C2×#17988835C2semidirect
8. C2×#17988834C2semidirect
9. C2×#17988791C2semidirect
10. C2×#17988728C2semidirect
11. C2×#17988727C2semidirect
12. C2×#17988674C2semidirect
13. C2×#17988662C2semidirect
14. C2×#17988595C2semidirect
15. C2×#17988594C2semidirect
16. C2×#485×C73C2semidirect
27. #17989250C22semidirect
45. #17988936C22semidirect
46. #17988931C22semidirect
47. #17988881C22semidirect
48. #17988835C22semidirect
49. #17988834C22semidirect
50. #17988791C22semidirect
51. #17988728C22semidirect
52. #17988727C22semidirect
53. #17988674C22semidirect
54. #17988662C22semidirect
57. #17988595C22semidirect
58. #17988594C22semidirect
71. #485×C73C22semidirect
392. C2×C73#3329semidirect
403. C2×#485D73semidirect
414. C73C2×#3329semidirect
447. #485C2×D73semidirect
791. C2#22622223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893002
C2×#179892502
#226222232
C2×#179889362
C2×#179889312
C2×#179888812
C2×#179888352
C2×#179888342
C2×#179887912
C2×#179887282
C2×#179887272
C2×#179886742
C2×#179886622
C2×#179885952
C2×#179885942
C2×#485×C732
C2×#332973