Finite Group Databasebeta

← C2×#22620802 #33956658

Subgroups — C2×#22620802 #33956658

Order 18688.

2314 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989160C211yesmaximal, characteristic, complemented
2C2×#17989156C211yesmaximal, characteristic
3#22620802C2116yesmaximal, direct product factor
4C2×#17988928C211yesmaximal, characteristic, complemented
5C2×#17988914C211yesmaximal, characteristic, complemented
6C2×#17988913C211yesmaximal, characteristic, complemented
7C2×#17988836C211yesmaximal, characteristic, complemented
8C2×#17988834C211yesmaximal, characteristic, complemented
9C2×#17988819C211yesmaximal, characteristic, complemented
10C2×#17988817C211yesmaximal, characteristic, complemented
11C2×#17988727C211yesmaximal, characteristic, complemented
12C2×#17988727C211yesmaximal, characteristic, complemented
13C2×#17988740C211yesmaximal, characteristic, complemented
14C2×#17988737C211yesmaximal, characteristic, complemented
15C2×#17988552C211yesmaximal, characteristic, complemented
16C2×#485×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic, complemented
19C23×D292C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22C22×#11924015C2211yescharacteristic
23C22×#11924015C2211yescharacteristic
24C22×#11924011C2211yescharacteristic, complemented
25C22×C8×D73C2211yescharacteristic, complemented
26#17989160—24no—
27#17989160C2218yescomplemented
28#17989156—24no—
29#17989156C2218yes—
30C2×#14556590—21no—
31C2×#14556588—21no—
32C2×#14556579—21no—
33C2×#14556577—21no—
34C2×#14556576—21no—
35C2×#14556573—21no—
36C2×#14556571C2211yescharacteristic, complemented
37C2×#14556570C2211yescharacteristic
38C2×#14556567C2211yescharacteristic, complemented
39C2×#14556566C2211yescharacteristic
40C2×#14556566C2211yescharacteristic
41C2×#14556566C2211yescharacteristic
42C2×#14556566C2211yescharacteristic
43C2×#14556561—21no—
44C2×#14556561—21no—
45C2×#14556549C2211yescharacteristic, complemented
46#17988928C2218yescomplemented
47#17988914C2218yescomplemented
48#17988913C2218yescomplemented
49#17988836C2218yescomplemented
50#17988834C2218yescomplemented
51#17988819C2218yescomplemented
52#17988817C2218yescomplemented
53#17988740C2218yescomplemented
54#17988737C2218yescomplemented
55#17988727C2218yescomplemented
56#17988727C2218yescomplemented
57C2×#14556524C2211yescharacteristic, complemented
58C2×#14556522C2211yescharacteristic, complemented
59C2×#14556514C2211yescharacteristic, complemented
60C2×#14556514C2211yescharacteristic, complemented
61C2×#14556513C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65#17988552C2218yescomplemented
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic, complemented
68C2×#14556503C2211yescharacteristic, complemented
69C2×C22⋊Q8×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71#485×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic, complemented
73C2×#106×C73C2211yescharacteristic, complemented
74C2×#103×C73C2211yescharacteristic, complemented
75C2×#103×C73C2211yescharacteristic, complemented
76C2×C22⋊C8×C73C2211yescharacteristic
77C24×D73—21no—
78C2×#11924028—42no—
79C2×#11924028—42no—
80C2×#11924028D414yes—
81C2×#11924028C2314yes—
82C22×Dic146—21no—
83C22×Dic146D411yescharacteristic
84C22×Dic146C2311yescharacteristic
85C2×Q8×D73—22no—
86C2×Q8×D73—42no—
87C2×Q8×D73—42no—
88C2×Q8×D73C2314yescomplemented
89C22×D292—21no—
90C22×D292—21no—
91C22×D292—21no—
92C22×D292—21no—
93C22×D292—21no—
94C22×D292—22no—
95C22×D292—42no—
96C22×D292—42no—
97C22×D292D411yescharacteristic
98C22×D292C2311yescharacteristic
99C22×D292C2311yescharacteristic
100C22×D292C2314yes—
101C22×C22⋊D73D411yescharacteristic
102C22×C22⋊D73D411yescharacteristic
103C22×C4×D73—21no—
104C22×C4×D73C2311yescharacteristic
105C22×C4×D73C2311yescharacteristic
106C2×#11924017—42no—
107C2×#11924017—42no—
108C2×#11924017C2314yes—
109C2×#11924017C2314yes—
110C2×#11924015—42no—
111C2×#11924015—42no—
112C2×#11924015C2314yes—
113C2×#11924015C2314yes—
114C2×#11924011—42no—
115C2×#11924011C2314yescomplemented
116C22×#10596831C2311yescharacteristic
117C22×#10596831C2311yescharacteristic
118C2×C8×D73—42no—
119C2×C8×D73C2314yescomplemented
120#14556590—28no—
121#14556588—28no—
122#14556579—28no—
123#14556577—28no—
124#14556576—28no—
125#14556573—28no—
126#14556571—22no—
127#14556571C2314yescomplemented
128#14556570—22no—
129#14556570C2314yes—
130#14556567—22no—
131#14556567C2314yescomplemented
132#14556566—22no—
133#14556566—22no—
134#14556566—22no—
135#14556566—22no—
136#14556566C2314yes—
137#14556566C2314yes—
138#14556566C2314yes—
139#14556566C2314yes—
140#14556561—28no—
141#14556561—28no—
142#14556549—22no—
143#14556549C2314yescomplemented
144C2×C4⋊Dic73—21no—
145C2×C4⋊Dic73C2311yescharacteristic
146C2×#11924007—21no—
147C2×#11924007—21no—
148C2×C22⋊Dic73—21no—
149C2×#11924005—21no—
150C2×#11924005—21no—
151C2×#11924005—21no—
152C2×#11924005—21no—
153C2×#11924005—21no—
154C2×#11924005—21no—
155C2×#11924005—21no—
156C2×C4×Dic73—21no—
157#14556524C2314yescomplemented
158#14556522C2314yescomplemented
159#14556514C2314yescomplemented
160#14556514C2314yescomplemented
161#14556513C2314yes—
162#14556513C2314yes—
163#14556511C2314yes—
164#14556511C2314yes—
165C22⋊#10596831C2314yes—
166#14556503C2314yescomplemented
167#14556503C2314yescomplemented
168C22×Q8×C73C2311yescharacteristic
169C23×C4×C73C2311yescharacteristic
170C22×C8×C73C2311yescharacteristic
171C22×C8×C73C2311yescharacteristic
172C22⋊Q8×C73—22no—
173C22⋊Q8×C73C2314yes—
174#117×C73—22no—
175#117×C73C2314yes—
176C2×C4⋊C4×C73—21no—
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C22⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182C2×C42×C73—21no—
183#107×C73C2314yescomplemented
184#106×C73C2314yescomplemented
185#103×C73C2314yescomplemented
186#103×C73C2314yescomplemented
187C22⋊C8×C73C2314yes—
188C23×D73—21no—
189C23×D73—21no—
190C23×D73—24no—
191C23×D73—44no—
192C23×D73—82no—
193C23×D73—82no—
194C23×D73C2×D411yescharacteristic
195C23×D73C2×D411yescharacteristic
196#11924028—48no—
197#11924028—44no—
198#11924028—44no—
199C2×Dic146—22no—
200C2×Dic146—22no—
201C2×Dic146—21no—
202C2×Dic146—24no—
203C2×Dic146—42no—
204C2×Dic146—44no—
205C2×Dic146C2×D414yes—
206C2×Dic146C2412yes—
207Q8×D73—44no—
208Q8×D73—44no—
209Q8×D73—48no—
210C2×D292—22no—
211C2×D292—22no—
212C2×D292—22no—
213C2×D292—22no—
214C2×D292—21no—
215C2×D292—21no—
216C2×D292—24no—
217C2×D292—24no—
218C2×D292—24no—
219C2×D292—24no—
220C2×D292—24no—
221C2×D292—44no—
222C2×D292—44no—
223C2×D292—42no—
224C2×D292—44no—
225C2×D292—48no—
226C2×D292—82no—
227C2×D292—82no—
228C2×D292—82no—
229C2×D292—82no—
230C2×D292C2×D414yes—
231C2×D292C2412yes—
232C2×D292C2412yes—
233C2×C22⋊D73—42no—
234C2×C22⋊D73—42no—
235C2×C22⋊D73C2×D414yes—
236C2×C22⋊D73C2×D414yes—
237C22×Dic73—21no—
238C22×Dic73—21no—
239C22×Dic73C2×D411yescharacteristic
240C22×Dic73C2×D411yescharacteristic
241C2×C4×D73—22no—
242C2×C4×D73—22no—
243C2×C4×D73—22no—
244C2×C4×D73—22no—
245C2×C4×D73—24no—
246C2×C4×D73—44no—
247C2×C4×D73C2×D412yes—
248C2×C4×D73C2×D412yes—
249C2×C4×D73C2412yes—
250C2×C4×D73C2412yes—
251#11924017—44no—
252#11924017—44no—
253#11924015—44no—
254#11924015—44no—
255#11924011—44no—
256C2×#10596831—22no—
257C2×#10596831—22no—
258C2×#10596831C2412yes—
259C2×#10596831C2412yes—
260C8×D73—44no—
261C4⋊Dic73—21no—
262C4⋊Dic73—24no—
263C4⋊Dic73C2412yes—
264#11924007—24no—
265#11924007—24no—
266C22⋊Dic73—24no—
267#11924005—24no—
268#11924005—24no—
269#11924005—24no—
270#11924005—24no—
271#11924005—24no—
272#11924005—24no—
273#11924005—24no—
274C4×Dic73—24no—
275C24×C73C2×D411yescharacteristic
276C2×Q8×C73—21no—
277C2×Q8×C73—22no—
278C2×Q8×C73—22no—
279C2×Q8×C73C2412yes—
280C22×C4×C73—22no—
281C22×C4×C73—22no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—21no—
285C22×C4×C73—21no—
286C22×C4×C73C2×D411yescharacteristic
287C22×C4×C73C2×D412yes—
288C22×C4×C73C2412yes—
289C22×C4×C73C2411yescharacteristic
290C2×C8×C73—22no—
291C2×C8×C73—22no—
292C2×C8×C73C2412yes—
293C2×C8×C73C2412yes—
294C4⋊C4×C73—24no—
295C4⋊C4×C73—21no—
296C4⋊C4×C73—21no—
297C4⋊C4×C73—21no—
298C4⋊C4×C73C2412yes—
299C4⋊C4×C73C2412yes—
300C4⋊C4×C73C2412yes—
301C22⋊C4×C73—24no—
302C22⋊C4×C73—24no—
303C42×C73—24no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73C22×D412yes—
308C23×C73C22×D411yescharacteristic
309C22×D73—22no—
310C22×D73—22no—
311C22×D73—22no—
312C22×D73—22no—
313C22×D73—22no—
314C22×D73—22no—
315C22×D73—22no—
316C22×D73—22no—
317C22×D73—48no—
318C22×D73—42no—
319C22×D73—42no—
320C22×D73—42no—
321C22×D73—42no—
322C22×D73—42no—
323C22×D73—42no—
324C22×D73—84no—
325C22×D73—84no—
326C22×D73—816no—
327C22×D73C22×D412yes—
328C22×D73C22×D412yes—
329Q8×C73—22no—
330Q8×C73—22no—
331Q8×C73—42no—
332C2×C4×C73—22no—
333C2×C4×C73—24no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—42no—
341C2×C4×C73—42no—
342C2×C4×C73—42no—
343C2×C4×C73—42no—
344C2×C4×C73C22×D412yes—
345C2×C4×C73C22×D411yescharacteristic
346C2×C4×C73H(5,𝔽2)12yes—
347C2×C4×C73H(5,𝔽2)12yes—
348C2×C4×C73C2511yescharacteristic
349C22⋊D73—44no—
350C22⋊D73—44no—
351C2×Dic73—22no—
352C2×Dic73—22no—
353C2×Dic73—22no—
354C2×Dic73—22no—
355C2×Dic73—42no—
356C2×Dic73—42no—
357C2×Dic73C22×D412yes—
358C2×Dic73C22×D412yes—
359D292—22no—
360D292—22no—
361D292—22no—
362D292—22no—
363D292—44no—
364D292—48no—
365D292—42no—
366D292—42no—
367D292—84no—
368D292—84no—
369D292—84no—
370D292—84no—
371C4×D73—24no—
372C4×D73—24no—
373C4×D73—22no—
374C4×D73—22no—
375C4×D73—22no—
376C4×D73—22no—
377C4×D73—48no—
378Dic146—22no—
379Dic146—22no—
380Dic146—44no—
381Dic146—48no—
382Dic146—42no—
383C8×C73—22no—
384C8×C73—22no—
385#10596831—22no—
386#10596831—22no—
387C22×C73—22no—
388C22×C73—22no—
389C22×C73—22no—
390C22×C73—44no—
391C22×C73#53412yes—
392C22×C73#57712yes—
393C22×C73#57712yes—
394C22×C73C23×D411yescharacteristic
395C2×D73—22no—
396C2×D73—22no—
397C2×D73—22no—
398C2×D73—22no—
399C2×D73—22no—
400C2×D73—22no—
401C2×D73—44no—
402C2×D73—44no—
403C2×D73—42no—
404C2×D73—42no—
405C2×D73—42no—
406C2×D73—42no—
407C2×D73—42no—
408C2×D73—42no—
409C2×D73—816no—
410C2×D73—84no—
411C2×D73—84no—
412C4×C73—22no—
413C4×C73—42no—
414C4×C73—42no—
415C4×C73—42no—
416C4×C73—42no—
417C4×C73#53412yes—
418C4×C73C2×H(5,𝔽2)11yescharacteristic
419C4×C73C2×H(5,𝔽2)11yescharacteristic
420Dic73—22no—
421Dic73—22no—
422Dic73—42no—
423Dic73—42no—
424C2×#3200—731nomaximal, Sylow
425C2×C73—42no—
426C2×C73#320014yescomplemented
427C2×C73C2×#53411yescharacteristic
428C2×C73C2×#57711yescharacteristic
429C2×C73C2×#57711yescharacteristic
430D73—42no—
431D73—42no—
432D73—82no—
433D73—82no—
434C2×#536—731no—
435C2×#535—731no—
436#3200—7316no—
437C2×#485—731no—
438C2×#485D7311yescharacteristic, complemented
439C2×#482—731no—
440C2×#482—731no—
441C2×#468—731no—
442C2×#468—731no—
443C2×#465—731no—
444C2×#465—731no—
445C2×#448—731no—
446C2×#448—731no—
447C2×#450—731no—
448C2×#450—731no—
449C2×#408—731no—
450C73C2×#320011yescharacteristic, complemented, Sylow
451C22×#41—731no—
452C23×Q8—731no—
453C23×D4—731no—
454C22×SD16—731no—
455C22×SD16—731no—
456C22×SD16—731no—
457C22×SD16—731no—
458C22×M16—731no—
459C23×C8—731no—
460#536—738no—
461#536—1464no—
462#535—738no—
463#535—1464no—
464C2×C4⋊Q8—1461no—
465C2×#127—1461no—
466C2×#124—1461no—
467C2×#124—1461no—
468C2×#123—1461no—
469C2×#123—1461no—
470C2×C22⋊Q8—731no—
471C2×C22⋊Q8—731no—
472C2×C22⋊Q8—731no—
473C2×C22⋊Q8C2×D7311yescharacteristic
474C2×#121—731no—
475C2×#121—731no—
476C2×#121—731no—
477C2×#121—731no—
478C2×#120—1461no—
479C2×#120—1461no—
480C2×#117—731no—
481C2×#117C2×D7311yescharacteristic
482#485—738no—
483#485C2×D7318yescomplemented
484#482—738no—
485#482—738no—
486#468—738no—
487#468—738no—
488#465—738no—
489#465—738no—
490#450—738no—
491#450—738no—
492#448—738no—
493#448—738no—
494C2×#107—731no—
495C2×#107C2×D7311yescharacteristic, complemented
496C2×#106—731no—
497C2×#106C2×D7311yescharacteristic, complemented
498C2×#103—731no—
499C2×#103—731no—
500C2×#103C2×D7311yescharacteristic, complemented
501C2×#103C2×D7311yescharacteristic, complemented
502C2×#102—731no—
503C2×#102—731no—
504C2×#102—731no—
505C2×#102—731no—
506#408—738no—
507C2×C22⋊C8—731no—
508C2×C22⋊C8—731no—
509C2×C22⋊C8—731no—
510C2×C22⋊C8C2×D7311yescharacteristic
511C25—1461no—
512C2×#41—2922no—
513C2×#41—2922no—
514C2×#41—734no—
515C2×#41—734no—
516C22×Q8—2922no—
517C22×Q8—2922no—
518C22×Q8—731no—
519C22×Q8—734no—
520C22×Q8—731no—
521C22×Q8—1461no—
522C22×Q8—1462no—
523C22×Q8C22×D7311yescharacteristic
524C22×D4—2922no—
525C22×D4—2922no—
526C22×D4—731no—
527C22×D4—731no—
528C22×D4—731no—
529C22×D4—734no—
530C22×D4—731no—
531C22×D4—731no—
532C22×D4—1461no—
533C22×D4—1461no—
534C22×D4—1461no—
535C22×D4—1461no—
536C22×D4—1461no—
537C22×D4—1462no—
538C23×C4—731no—
539C23×C4—731no—
540C23×C4—1461no—
541C23×C4C22×D7311yescharacteristic
542C2×SD16—2922no—
543C2×SD16—2922no—
544C2×SD16—2922no—
545C2×SD16—2922no—
546C2×SD16—734no—
547C2×SD16—734no—
548C2×SD16—734no—
549C2×SD16—734no—
550C2×M16—2922no—
551C2×M16—734no—
552C22×C8—2922no—
553C22×C8—734no—
554C22×C8—731no—
555C22×C8—731no—
556C22×C8C22×D7311yescharacteristic
557C22×C8C22×D7311yescharacteristic
558C4⋊Q8—1468no—
559#127—1468no—
560#124—1468no—
561#124—1468no—
562#123—1468no—
563#123—1468no—
564C22⋊Q8—22no—
565C22⋊Q8—734no—
566C22⋊Q8—734no—
567C22⋊Q8—734no—
568C22⋊Q8—1462no—
569C22⋊Q8—1462no—
570C22⋊Q8—1462no—
571C22⋊Q8C22×D7314yes—
572#121—734no—
573#121—734no—
574#121—734no—
575#121—734no—
576#121—1462no—
577#121—1462no—
578#121—1462no—
579#121—1462no—
580#120—1468no—
581#120—1468no—
582#117—22no—
583#117—734no—
584#117—1462no—
585#117C22×D7314yes—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—731no—
588C2×C4⋊C4—1461no—
589C2×C4⋊C4—1461no—
590C2×C4⋊C4—1461no—
591C2×C4⋊C4C22×D7311yescharacteristic
592C2×C4⋊C4C22×D7311yescharacteristic
593C2×C4⋊C4C22×D7311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1461no—
597C2×C22⋊C4—1461no—
598C2×C22⋊C4—1461no—
599C2×C22⋊C4—1461no—
600C2×C22⋊C4—1461no—
601C2×C22⋊C4—1461no—
602C2×C22⋊C4—1461no—
603C2×C22⋊C4—1461no—
604C2×C42—21no—
605C2×C42—1461no—
606#107—734no—
607#107C22×D7314yescomplemented
608#106—734no—
609#106C22×D7314yescomplemented
610#103—734no—
611#103—734no—
612#103C22×D7314yescomplemented
613#103C22×D7314yescomplemented
614#102—734no—
615#102—734no—
616#102—734no—
617#102—734no—
618C22⋊C8—734no—
619C22⋊C8—734no—
620C22⋊C8—734no—
621C22⋊C8C22×D7314yes—
622C24—2924no—
623C24—5842no—
624C24—5842no—
625C24—731no—
626C24—731no—
627C24—1461no—
628C24—1461no—
629C24—1464no—
630C24D4×D7311yescharacteristic
631#41—2928no—
632#41—2924no—
633#41—2924no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—2922no—
638C2×Q8—2924no—
639C2×Q8—2924no—
640C2×Q8—2924no—
641C2×Q8—2928no—
642C2×Q8—734no—
643C2×Q8—732no—
644C2×Q8—1464no—
645C2×Q8—1462no—
646C2×Q8—1462no—
647C2×Q8—1461no—
648C2×Q8C23×D7312yes—
649C2×D4—2924no—
650C2×D4—2928no—
651C2×D4—2922no—
652C2×D4—2924no—
653C2×D4—2924no—
654C2×D4—2922no—
655C2×D4—2922no—
656C2×D4—5842no—
657C2×D4—5842no—
658C2×D4—5842no—
659C2×D4—5842no—
660C2×D4—734no—
661C2×D4—734no—
662C2×D4—734no—
663C2×D4—732no—
664C2×D4—732no—
665C2×D4—1464no—
666C2×D4—1464no—
667C2×D4—1464no—
668C2×D4—1464no—
669C2×D4—1461no—
670C2×D4—1461no—
671C2×D4—1464no—
672C2×D4—1462no—
673C2×D4—1462no—
674C2×D4—1462no—
675C2×D4—1462no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—2924no—
683C22×C4—731no—
684C22×C4—731no—
685C22×C4—732no—
686C22×C4—732no—
687C22×C4—732no—
688C22×C4—732no—
689C22×C4—1464no—
690C22×C4—1461no—
691C22×C4—1461no—
692C22×C4—1462no—
693C22×C4—1462no—
694C22×C4—1462no—
695C22×C4—1462no—
696C22×C4D4×D7312yes—
697C22×C4D4×D7311yescharacteristic
698C22×C4C23×D7312yes—
699C22×C4C23×D7311yescharacteristic
700SD16—2924no—
701SD16—2924no—
702SD16—2924no—
703SD16—2924no—
704M16—2924no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—2924no—
708C2×C8—732no—
709C2×C8—732no—
710C2×C8—1462no—
711C2×C8—1462no—
712C2×C8C23×D7312yes—
713C2×C8C23×D7312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—732no—
719C4⋊C4—1464no—
720C4⋊C4—1464no—
721C4⋊C4—1464no—
722C4⋊C4—1461no—
723C4⋊C4C23×D7312yes—
724C4⋊C4C23×D7312yes—
725C4⋊C4C23×D7312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—1464no—
729C22⋊C4—1464no—
730C22⋊C4—1464no—
731C22⋊C4—1464no—
732C22⋊C4—1464no—
733C22⋊C4—1464no—
734C22⋊C4—1464no—
735C22⋊C4—1464no—
736C42—24no—
737C42—1464no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—2928no—
742C23—2922no—
743C23—2922no—
744C23—2922no—
745C23—2922no—
746C23—2922no—
747C23—2922no—
748C23—5844no—
749C23—5844no—
750C23—58416no—
751C23—732no—
752C23—732no—
753C23—1462no—
754C23—1462no—
755C23—1462no—
756C23—1462no—
757C23—1462no—
758C23—1462no—
759C23—1462no—
760C23—1462no—
761C23C2×D4×D7312yes—
762C23C2×D4×D7311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—2924no—
767Q8—2928no—
768Q8—2922no—
769Q8—1462no—
770Q8—1462no—
771D4—2928no—
772D4—2924no—
773D4—2924no—
774D4—2924no—
775D4—2922no—
776D4—2922no—
777D4—5844no—
778D4—5844no—
779D4—5844no—
780D4—5844no—
781D4—1462no—
782D4—1462no—
783D4—1462no—
784D4—1462no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—2928no—
798C2×C4—2922no—
799C2×C4—2922no—
800C2×C4—732no—
801C2×C4—732no—
802C2×C4—1462no—
803C2×C4—1462no—
804C2×C4—1462no—
805C2×C4—1462no—
806C2×C4—1464no—
807C2×C4—1464no—
808C2×C4—1462no—
809C2×C4—1462no—
810C2×C4—1462no—
811C2×C4—1462no—
812C2×C4C2×D4×D7312yes—
813C2×C4C2×D4×D7311yescharacteristic
814C2×C4#1455663712yes—
815C2×C4#1455663712yes—
816C2×C4C24×D7311yescharacteristic
817C8—22no—
818C8—22no—
819C8—1462no—
820C8—1462no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—2924no—
826C22—2924no—
827C22—2922no—
828C22—2922no—
829C22—2922no—
830C22—2922no—
831C22—2922no—
832C22—2922no—
833C22—58416no—
834C22—5844no—
835C22—5844no—
836C22—1462no—
837C22—1462no—
838C22—1462no—
839C22—1462no—
840C22—1462no—
841C22—1462no—
842C22#1798914812yes—
843C22#1798939412yes—
844C22#1798939612yes—
845C22C22×D4×D7311yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—2922no—
852C4—2922no—
853C4—1462no—
854C4—1462no—
855C4#1798914812yes—
856C4C2×#1455663711yescharacteristic
857C4C2×#1455663711yescharacteristic
858C2—42no—
859C2—2922no—
860C2—2922no—
861C2—5842no—
862C2—5842no—
863C2#2262080214yesdirect product factor
864C2C2×#1798914811yescharacteristic
865C2C2×#1798939411yescharacteristic
866C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#485×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989156C2
hypercenterC2×#485D73
hypocenterC73C2×#3200
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
1. C2×#17989160C2semidirect
3. #22620802C2direct (N × H)
4. C2×#17988928C2semidirect
5. C2×#17988914C2semidirect
6. C2×#17988913C2semidirect
7. C2×#17988836C2semidirect
8. C2×#17988834C2semidirect
9. C2×#17988819C2semidirect
10. C2×#17988817C2semidirect
11. C2×#17988727C2semidirect
12. C2×#17988727C2semidirect
13. C2×#17988740C2semidirect
14. C2×#17988737C2semidirect
15. C2×#17988552C2semidirect
16. C2×#485×C73C2semidirect
18. C22×Q8×D73C22semidirect
24. C22×#11924011C22semidirect
25. C22×C8×D73C22semidirect
27. #17989160C22semidirect
36. C2×#14556571C22semidirect
38. C2×#14556567C22semidirect
45. C2×#14556549C22semidirect
46. #17988928C22semidirect
47. #17988914C22semidirect
48. #17988913C22semidirect
49. #17988836C22semidirect
50. #17988834C22semidirect
51. #17988819C22semidirect
52. #17988817C22semidirect
53. #17988740C22semidirect
54. #17988737C22semidirect
55. #17988727C22semidirect
56. #17988727C22semidirect
57. C2×#14556524C22semidirect
58. C2×#14556522C22semidirect
59. C2×#14556514C22semidirect
60. C2×#14556514C22semidirect
65. #17988552C22semidirect
67. C2×#14556503C22semidirect
68. C2×#14556503C22semidirect
71. #485×C73C22semidirect
72. C2×#107×C73C22semidirect
73. C2×#106×C73C22semidirect
74. C2×#103×C73C22semidirect
75. C2×#103×C73C22semidirect
88. C2×Q8×D73C23semidirect
115. C2×#11924011C23semidirect
119. C2×C8×D73C23semidirect
127. #14556571C23semidirect
131. #14556567C23semidirect
143. #14556549C23semidirect
157. #14556524C23semidirect
158. #14556522C23semidirect
159. #14556514C23semidirect
160. #14556514C23semidirect
166. #14556503C23semidirect
167. #14556503C23semidirect
183. #107×C73C23semidirect
184. #106×C73C23semidirect
185. #103×C73C23semidirect
186. #103×C73C23semidirect
426. C2×C73#3200semidirect
438. C2×#485D73semidirect
450. C73C2×#3200semidirect
483. #485C2×D73semidirect
495. C2×#107C2×D73semidirect
497. C2×#106C2×D73semidirect
500. C2×#103C2×D73semidirect
501. C2×#103C2×D73semidirect
607. #107C22×D73semidirect
609. #106C22×D73semidirect
612. #103C22×D73semidirect
613. #103C22×D73semidirect
863. C2#22620802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891602
C2×#179891562
#226208022
C2×#179889282
C2×#179889142
C2×#179889132
C2×#179888362
C2×#179888342
C2×#179888192
C2×#179888172
C2×#179887272
C2×#179887402
C2×#179887372
C2×#179885522
C2×#485×C732
C2×#320073