Finite Group Databasebeta

← C2×#22621931 #33962680

Subgroups — C2×#22621931 #33962680

Order 18688.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989258C211yesmaximal, characteristic, complemented
2#22621931C2116yesmaximal, direct product factor
3C2×#17988953C211yesmaximal, characteristic, complemented
4C2×#17988911C211yesmaximal, characteristic, complemented
5C2×#17988900C211yesmaximal, characteristic, complemented
6C2×#17988891C211yesmaximal, characteristic, complemented
7C2×#17988838C211yesmaximal, characteristic, complemented
8C2×#17988821C211yesmaximal, characteristic, complemented
9C2×#17988782C211yesmaximal, characteristic, complemented
10C2×#17988730C211yesmaximal, characteristic, complemented
11C2×#17988730C211yesmaximal, characteristic, complemented
12C2×#17988687C211yesmaximal, characteristic, complemented
13C2×#17988659C211yesmaximal, characteristic, complemented
14C2×#17988586C211yesmaximal, characteristic, complemented
15C2×#17988581C211yesmaximal, characteristic, complemented
16C2×#553×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×#11924028C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924013C2211yescharacteristic
21C22×#11924013C2211yescharacteristic
22C22×#11924012C2211yescharacteristic
23C23×#10596831C2211yescharacteristic
24#17989258—24no—
25#17989258C2218yescomplemented
26C2×#14556588C2211yescharacteristic
27C2×#14556587—21no—
28C2×#14556565C2211yescharacteristic
29C2×#14556565C2211yescharacteristic
30C2×#14556564—21no—
31C2×#14556564—21no—
32C2×C4×Dic146C2211yescharacteristic
33C2×#14556553—21no—
34#17988953C2218yescomplemented
35#17988911C2218yescomplemented
36#17988900C2218yescomplemented
37#17988891C2218yescomplemented
38#17988838C2218yescomplemented
39#17988821C2218yescomplemented
40#17988782C2218yescomplemented
41#17988730C2218yescomplemented
42#17988730C2218yescomplemented
43#17988687C2218yescomplemented
44#17988659C2218yescomplemented
45C2×#14556524C2211yescharacteristic
46C2×#14556524C2211yescharacteristic
47C2×#14556522C2211yescharacteristic
48C2×C4⋊#10596831C2211yescharacteristic
49#17988586C2218yescomplemented
50#17988581C2218yescomplemented
51C2×#14556514C2211yescharacteristic
52C2×#14556514C2211yescharacteristic
53C2×#14556514C2211yescharacteristic
54C2×#14556512C2211yescharacteristic
55C2×#14556511C2211yescharacteristic
56C2×#14556511C2211yescharacteristic
57C2×#14556511C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×C22⋊#10596831C2211yescharacteristic
63C2×#14556502C2211yescharacteristic
64#553×C73—24no—
65#553×C73C2218yescomplemented
66C2×#126×C73—21no—
67C2×#125×C73C2211yescharacteristic
68C2×#123×C73—21no—
69C2×#121×C73—21no—
70C2×#121×C73C2211yescharacteristic
71C2×#121×C73C2211yescharacteristic
72C2×C4×D4×C73—21no—
73C2×C4×D4×C73C2211yescharacteristic
74C2×C4×D4×C73C2211yescharacteristic
75C2×#117×C73C2211yescharacteristic
76C22×C4⋊C4×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—24no—
79C2×#11924028—22no—
80C2×#11924028—22no—
81C2×#11924028—42no—
82C2×#11924028—42no—
83C2×#11924028C2314yes—
84C2×#11924028C2314yes—
85C22×Dic146C2311yescharacteristic
86C22×D292—21no—
87C22×D292—21no—
88C22×D292C2311yescharacteristic
89C22×D292C2311yescharacteristic
90C22×C22⋊D73—21no—
91C22×C22⋊D73—21no—
92C22×C22⋊D73—21no—
93C22×C22⋊D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73—21no—
96C2×#11924016—24no—
97C2×#11924016C2314yes—
98C2×#11924013—42no—
99C2×#11924013—42no—
100C2×#11924013C2314yes—
101C2×#11924013C2314yes—
102C2×#11924012—42no—
103C2×#11924012C2314yes—
104C22×#10596831—42no—
105C22×#10596831C2311yescharacteristic
106C22×#10596831C2311yescharacteristic
107C22×#10596831C2311yescharacteristic
108C22×#10596831C2311yescharacteristic
109C22×#10596831C2314yes—
110#14556588—22no—
111#14556588C2314yes—
112#14556587—28no—
113#14556565—22no—
114#14556565—22no—
115#14556565C2314yes—
116#14556565C2314yes—
117#14556564—28no—
118#14556564—28no—
119C4×Dic146—22no—
120C4×Dic146C2314yes—
121#14556553—28no—
122C2×C4⋊Dic73C2311yescharacteristic
123C2×#11924007—21no—
124C2×#11924005—21no—
125C2×#11924005—21no—
126C2×C4×Dic73—21no—
127#14556524C2314yes—
128#14556524C2314yes—
129#14556522C2314yes—
130C4⋊#10596831C2314yes—
131#14556514C2314yes—
132#14556514C2314yes—
133#14556514C2314yes—
134#14556512C2314yes—
135#14556511C2314yes—
136#14556511C2314yes—
137#14556511C2314yes—
138#14556511C2314yes—
139#14556511C2314yes—
140#14556511C2314yes—
141C22⋊#10596831C2314yes—
142C22⋊#10596831C2314yes—
143#14556502C2314yes—
144C22×D4×C73—21no—
145C22×D4×C73—21no—
146C22×D4×C73D411yescharacteristic
147C22×D4×C73C2311yescharacteristic
148C23×C4×C73—21no—
149C23×C4×C73—21no—
150C23×C4×C73C2311yescharacteristic
151C23×C4×C73C2311yescharacteristic
152#126×C73—28no—
153#125×C73—22no—
154#125×C73C2314yes—
155#123×C73—28no—
156#121×C73—28no—
157#121×C73—22no—
158#121×C73—22no—
159#121×C73C2314yes—
160#121×C73C2314yes—
161C4×D4×C73—28no—
162C4×D4×C73—22no—
163C4×D4×C73D414yes—
164C4×D4×C73C2314yes—
165C4×D4×C73C2314yes—
166#117×C73—22no—
167#117×C73C2314yes—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—22no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73D411yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C4⋊C4×C73C2314yes—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C22⋊C4×C73—21no—
181C2×C22⋊C4×C73D411yescharacteristic
182C2×C22⋊C4×C73D411yescharacteristic
183C2×C42×C73—21no—
184C2×C42×C73C2311yescharacteristic
185C23×D73—21no—
186C23×D73—21no—
187#11924028—28no—
188#11924028—28no—
189#11924028—44no—
190#11924028—44no—
191#11924028—48no—
192#11924028—48no—
193C2×Dic146—21no—
194C2×Dic146—22no—
195C2×Dic146#4114yes—
196C2×Dic146C2412yes—
197C2×D292—22no—
198C2×D292—22no—
199C2×D292—22no—
200C2×D292—22no—
201C2×D292—24no—
202C2×D292—21no—
203C2×D292—21no—
204C2×D292—24no—
205C2×D292—44no—
206C2×D292—82no—
207C2×D292C2412yes—
208C2×D292C2412yes—
209C2×C22⋊D73—24no—
210C2×C22⋊D73—24no—
211C2×C22⋊D73—24no—
212C2×C22⋊D73—24no—
213C2×C22⋊D73—44no—
214C2×C22⋊D73—44no—
215C2×C22⋊D73—82no—
216C2×C22⋊D73—82no—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C2×C4×D73—24no—
220C2×C4×D73—24no—
221C2×C4×D73—44no—
222C2×C4×D73—44no—
223#11924016—28no—
224#11924013—44no—
225#11924013—44no—
226#11924012—44no—
227C2×#10596831—22no—
228C2×#10596831—22no—
229C2×#10596831—22no—
230C2×#10596831—22no—
231C2×#10596831—44no—
232C2×#10596831C2412yes—
233C2×#10596831C2412yes—
234C2×#10596831C2412yes—
235C2×#10596831C2412yes—
236C4⋊Dic73—21no—
237C4⋊Dic73C2412yes—
238#11924007—24no—
239#11924005—24no—
240#11924005—24no—
241C4×Dic73—24no—
242C24×C73—21no—
243C24×C73C2×D411yescharacteristic
244C24×C73C2×D411yescharacteristic
245C2×D4×C73—24no—
246C2×D4×C73—24no—
247C2×D4×C73—21no—
248C2×D4×C73—22no—
249C2×D4×C73—22no—
250C2×D4×C73—42no—
251C2×D4×C73—44no—
252C2×D4×C73—82no—
253C2×D4×C73C2×D414yes—
254C2×D4×C73C2412yes—
255C22×C4×C73—22no—
256C22×C4×C73—22no—
257C22×C4×C73—22no—
258C22×C4×C73—22no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—24no—
263C22×C4×C73—24no—
264C22×C4×C73—82no—
265C22×C4×C73—82no—
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2×D412yes—
271C22×C4×C73C2×D412yes—
272C22×C4×C73C2412yes—
273C22×C4×C73C2412yes—
274C22×C4×C73C2411yescharacteristic
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73—24no—
278C4⋊C4×C73—24no—
279C4⋊C4×C73—24no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73C2×D414yes—
282C4⋊C4×C73C2412yes—
283C4⋊C4×C73C2412yes—
284C4⋊C4×C73C2412yes—
285C22⋊C4×C73—24no—
286C22⋊C4×C73—24no—
287C22⋊C4×C73—24no—
288C22⋊C4×C73—24no—
289C22⋊C4×C73C2×D414yes—
290C22⋊C4×C73C2×D414yes—
291C42×C73—24no—
292C42×C73C2×D412yes—
293C42×C73C2412yes—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73—22no—
301C23×C73—42no—
302C23×C73—42no—
303C23×C73—42no—
304C23×C73C22×D412yes—
305C23×C73C22×D412yes—
306C23×C73C22×D411yescharacteristic
307C22×D73—22no—
308C22×D73—22no—
309C22×D73—42no—
310C22×D73—42no—
311C22×D73—42no—
312C22×D73—42no—
313C22×D73—42no—
314C22×D73—42no—
315D4×C73—22no—
316D4×C73—22no—
317D4×C73—44no—
318D4×C73—48no—
319D4×C73—42no—
320D4×C73—84no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—24no—
326C2×C4×C73—24no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—42no—
335C2×C4×C73—42no—
336C2×C4×C73—42no—
337C2×C4×C73—84no—
338C2×C4×C73—84no—
339C2×C4×C73C22×D412yes—
340C2×C4×C73C22×D412yes—
341C2×C4×C73C22×D412yes—
342C2×C4×C73C22×D412yes—
343C2×C4×C73C22×D411yescharacteristic
344C2×C4×C73C2×#4112yes—
345C2×C4×C73H(5,𝔽2)12yes—
346C2×C4×C73C2511yescharacteristic
347C22⋊D73—48no—
348C22⋊D73—48no—
349C22⋊D73—84no—
350C22⋊D73—84no—
351C2×Dic73—24no—
352C2×Dic73—22no—
353C2×Dic73—22no—
354C2×Dic73—42no—
355D292—22no—
356D292—22no—
357D292—22no—
358D292—22no—
359D292—48no—
360D292—42no—
361D292—42no—
362D292—84no—
363C4×D73—48no—
364C4×D73—48no—
365Dic146—24no—
366Dic146—22no—
367Dic146C2×#4114yes—
368#10596831—22no—
369#10596831—22no—
370#10596831—22no—
371#10596831—22no—
372C22×C73—22no—
373C22×C73—22no—
374C22×C73—22no—
375C22×C73—22no—
376C22×C73—22no—
377C22×C73—22no—
378C22×C73—44no—
379C22×C73—44no—
380C22×C73—42no—
381C22×C73—42no—
382C22×C73—42no—
383C22×C73—84no—
384C22×C73#54612yes—
385C22×C73#57512yes—
386C22×C73#57612yes—
387C22×C73C23×D411yescharacteristic
388C2×D73—42no—
389C2×D73—42no—
390C2×D73—42no—
391C2×D73—42no—
392C2×D73—42no—
393C2×D73—42no—
394C2×D73—84no—
395C2×D73—84no—
396C4×C73—22no—
397C4×C73—22no—
398C4×C73—22no—
399C4×C73—22no—
400C4×C73—42no—
401C4×C73—42no—
402C4×C73—42no—
403C4×C73#54612yes—
404C4×C73C22×#4111yescharacteristic
405C4×C73C2×H(5,𝔽2)11yescharacteristic
406Dic73—24no—
407Dic73—42no—
408C2×#3309—731nomaximal, Sylow
409C2×C73—42no—
410C2×C73—42no—
411C2×C73—82no—
412C2×C73#330914yescomplemented
413C2×C73C2×#54611yescharacteristic
414C2×C73C2×#57511yescharacteristic
415C2×C73C2×#57611yescharacteristic
416D73—82no—
417D73—82no—
418C2×#553D7311yescharacteristic, complemented
419C2×#550—731no—
420#3309—7316no—
421C2×#490—731no—
422C2×#482—731no—
423C2×#480—731no—
424C2×#479—731no—
425C2×#469—731no—
426C2×#466—731no—
427C2×#459—731no—
428C2×#449—731no—
429C2×#449—731no—
430C2×#440—731no—
431C2×#435—731no—
432C2×#417—731no—
433C2×#416—731no—
434C73C2×#330911yescharacteristic, complemented, Sylow
435C22×#41—731no—
436C22×#41—731no—
437C22×SD16—731no—
438C22×D8—731no—
439C22×D8—731no—
440C22×M16—731no—
441C23×C8—731no—
442#553—24no—
443#553C2×D7318yescomplemented
444#550—738no—
445#550—1464no—
446C2×#127—731no—
447C2×#127—1461no—
448C2×#126—21no—
449C2×#125C2×D7311yescharacteristic
450C2×#123—21no—
451C2×#121—21no—
452C2×#121—731no—
453C2×#121—731no—
454C2×#121—1461no—
455C2×#121—1461no—
456C2×#121C2×D7311yescharacteristic
457C2×#121C2×D7311yescharacteristic
458C2×C4×Q8—731no—
459C2×C4×D4—21no—
460C2×C4×D4—1461no—
461C2×C4×D4C2×D7311yescharacteristic
462C2×C4×D4C2×D7311yescharacteristic
463C2×#117C2×D7311yescharacteristic
464C22×C4⋊C4C2×D7311yescharacteristic
465#490—738no—
466#482—738no—
467#480—738no—
468#479—738no—
469#469—738no—
470#466—738no—
471#459—738no—
472#449—738no—
473#449—738no—
474#440—738no—
475#435—738no—
476C2×#107—731no—
477C2×#107—731no—
478C2×#106—731no—
479C2×C4⋊C8—731no—
480#417—738no—
481#416—738no—
482C2×#103—731no—
483C2×#103—731no—
484C2×#103—731no—
485C2×#102—731no—
486C2×#102—731no—
487C2×#102—731no—
488C2×#102—731no—
489C2×#102—731no—
490C2×#102—731no—
491C2×#102—731no—
492C2×C22⋊C8—731no—
493C2×C22⋊C8—731no—
494C2×#97—731no—
495C2×#41—2922no—
496C2×#41—2922no—
497C2×#41—734no—
498C2×#41—734no—
499C2×#41—1464no—
500C2×#41—1464no—
501C2×#41—1462no—
502C2×#41—1462no—
503C22×Q8—731no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—731no—
507C22×D4—731no—
508C22×D4—1461no—
509C22×D4—1461no—
510C22×D4—1461no—
511C22×D4—1461no—
512C22×D4—1461no—
513C22×D4—1461no—
514C22×D4C22⋊D7311yescharacteristic
515C22×D4C22×D7311yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—1461no—
519C23×C4—1461no—
520C23×C4C22×D7311yescharacteristic
521C23×C4C22×D7311yescharacteristic
522C2×SD16—734no—
523C2×SD16—1464no—
524C2×D8—2922no—
525C2×D8—2922no—
526C2×D8—734no—
527C2×D8—734no—
528C2×M16—2922no—
529C2×M16—734no—
530C22×C8—2922no—
531C22×C8—734no—
532C22×C8—731no—
533C22×C8—731no—
534C22×C8—731no—
535C22×C8—731no—
536#127—734no—
537#127—1468no—
538#127—1462no—
539#126—28no—
540#125—22no—
541#125C22×D7314yes—
542#123—28no—
543#121—28no—
544#121—22no—
545#121—22no—
546#121—734no—
547#121—734no—
548#121—1462no—
549#121—1462no—
550#121—1468no—
551#121—1468no—
552#121C22×D7314yes—
553#121C22×D7314yes—
554C4×Q8—734no—
555C4×Q8—1462no—
556C4×D4—28no—
557C4×D4—22no—
558C4×D4—1468no—
559C4×D4C22⋊D7314yes—
560C4×D4C22×D7314yes—
561C4×D4C22×D7314yes—
562#117—22no—
563#117C22×D7314yes—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—731no—
569C2×C4⋊C4—1461no—
570C2×C4⋊C4C22⋊D7311yescharacteristic
571C2×C4⋊C4C22×D7311yescharacteristic
572C2×C4⋊C4C22×D7311yescharacteristic
573C2×C4⋊C4C22×D7314yes—
574C2×C4⋊C4C22×D7311yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—1461no—
580C2×C22⋊C4—1461no—
581C2×C22⋊C4C22⋊D7311yescharacteristic
582C2×C22⋊C4C22⋊D7311yescharacteristic
583C2×C42—21no—
584C2×C42—1461no—
585C2×C42C22×D7311yescharacteristic
586#107—734no—
587#107—734no—
588#106—734no—
589C4⋊C8—734no—
590#103—734no—
591#103—734no—
592#103—734no—
593#102—734no—
594#102—734no—
595#102—734no—
596#102—734no—
597#102—734no—
598#102—734no—
599#102—734no—
600C22⋊C8—734no—
601C22⋊C8—734no—
602#97—734no—
603C24—21no—
604C24—1461no—
605C24—1461no—
606C24C2×C22⋊D7311yescharacteristic
607C24C2×C22⋊D7311yescharacteristic
608#41—2928no—
609#41—2928no—
610#41—2924no—
611#41—2924no—
612#41—1468no—
613#41—1468no—
614C2×Q8—734no—
615C2×Q8—732no—
616C2×Q8—1461no—
617C2×Q8—1462no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—42no—
624C2×D4—44no—
625C2×D4—82no—
626C2×D4—2924no—
627C2×D4—2924no—
628C2×D4—2924no—
629C2×D4—5842no—
630C2×D4—5842no—
631C2×D4—5842no—
632C2×D4—732no—
633C2×D4—732no—
634C2×D4—1464no—
635C2×D4—1464no—
636C2×D4—1464no—
637C2×D4—1464no—
638C2×D4—1464no—
639C2×D4—1461no—
640C2×D4—1461no—
641C2×D4—1464no—
642C2×D4—1462no—
643C2×D4—1462no—
644C2×D4—1462no—
645C2×D4—1462no—
646C2×D4C2×C22⋊D7314yes—
647C2×D4C23×D7312yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—82no—
658C22×C4—82no—
659C22×C4—2924no—
660C22×C4—2924no—
661C22×C4—1461no—
662C22×C4—1464no—
663C22×C4—1464no—
664C22×C4—1461no—
665C22×C4C2×C22⋊D7312yes—
666C22×C4C2×C22⋊D7312yes—
667C22×C4C2×C22⋊D7311yescharacteristic
668C22×C4C2×C22⋊D7311yescharacteristic
669C22×C4C2×C22⋊D7311yescharacteristic
670C22×C4C2×C22⋊D7311yescharacteristic
671C22×C4C23×D7312yes—
672C22×C4C23×D7312yes—
673C22×C4C23×D7311yescharacteristic
674SD16—1468no—
675D8—2924no—
676D8—2924no—
677M16—2924no—
678C2×C8—2924no—
679C2×C8—732no—
680C2×C8—732no—
681C2×C8—732no—
682C2×C8—732no—
683C2×C8—1462no—
684C2×C8—1462no—
685C2×C8—1462no—
686C2×C8—1462no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—732no—
694C4⋊C4—1464no—
695C4⋊C4—1461no—
696C4⋊C4C2×C22⋊D7314yes—
697C4⋊C4C23×D7312yes—
698C4⋊C4C23×D7312yes—
699C4⋊C4C23×D7312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—1464no—
705C22⋊C4—1464no—
706C22⋊C4C2×C22⋊D7314yes—
707C22⋊C4C2×C22⋊D7314yes—
708C42—24no—
709C42—1464no—
710C42C2×C22⋊D7312yes—
711C42C23×D7312yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—2922no—
723C23—2922no—
724C23—2922no—
725C23—2922no—
726C23—2922no—
727C23—2922no—
728C23—1462no—
729C23—1462no—
730C23C22×C22⋊D7312yes—
731C23C22×C22⋊D7312yes—
732C23C22×C22⋊D7311yescharacteristic
733Q8—734no—
734Q8—1462no—
735Q8—1464no—
736D4—22no—
737D4—22no—
738D4—44no—
739D4—48no—
740D4—42no—
741D4—84no—
742D4—2928no—
743D4—2928no—
744D4—2928no—
745D4—2922no—
746D4—2922no—
747D4—5844no—
748D4—5844no—
749D4—5844no—
750D4—1462no—
751D4—1462no—
752D4—1462no—
753D4—1462no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—2928no—
773C2×C4—2928no—
774C2×C4—2922no—
775C2×C4—1462no—
776C2×C4—1462no—
777C2×C4—1464no—
778C2×C4C22×C22⋊D7312yes—
779C2×C4C22×C22⋊D7312yes—
780C2×C4C22×C22⋊D7312yes—
781C2×C4C22×C22⋊D7312yes—
782C2×C4C22×C22⋊D7311yescharacteristic
783C2×C4#41×D7312yes—
784C2×C4#1455663712yes—
785C2×C4C24×D7311yescharacteristic
786C8—1462no—
787C8—1462no—
788C8—1462no—
789C8—1462no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—2922no—
803C22—2922no—
804C22—2922no—
805C22—2922no—
806C22—2922no—
807C22—2922no—
808C22—5844no—
809C22—5844no—
810C22#1798922512yes—
811C22#1798938512yes—
812C22#1798939012yes—
813C22C23×C22⋊D7311yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—2922no—
822C4—1464no—
823C4#1798922512yes—
824C4C2×#41×D7311yescharacteristic
825C4C2×#1455663711yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—5842no—
830C2—5842no—
831C2#2262193114yesdirect product factor
832C2C2×#1798922511yescharacteristic
833C2C2×#1798938511yescharacteristic
834C2C2×#1798939011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#553×C73C2
socleC23×C73C22×D4
hypercenterC2×#553D73
hypocenterC73C2×#3309
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#17989258C2semidirect
2. #22621931C2direct (N × H)
3. C2×#17988953C2semidirect
4. C2×#17988911C2semidirect
5. C2×#17988900C2semidirect
6. C2×#17988891C2semidirect
7. C2×#17988838C2semidirect
8. C2×#17988821C2semidirect
9. C2×#17988782C2semidirect
10. C2×#17988730C2semidirect
11. C2×#17988730C2semidirect
12. C2×#17988687C2semidirect
13. C2×#17988659C2semidirect
14. C2×#17988586C2semidirect
15. C2×#17988581C2semidirect
16. C2×#553×C73C2semidirect
25. #17989258C22semidirect
34. #17988953C22semidirect
35. #17988911C22semidirect
36. #17988900C22semidirect
37. #17988891C22semidirect
38. #17988838C22semidirect
39. #17988821C22semidirect
40. #17988782C22semidirect
41. #17988730C22semidirect
42. #17988730C22semidirect
43. #17988687C22semidirect
44. #17988659C22semidirect
49. #17988586C22semidirect
50. #17988581C22semidirect
65. #553×C73C22semidirect
412. C2×C73#3309semidirect
418. C2×#553D73semidirect
434. C73C2×#3309semidirect
443. #553C2×D73semidirect
831. C2#22621931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892582
#226219312
C2×#179889532
C2×#179889112
C2×#179889002
C2×#179888912
C2×#179888382
C2×#179888212
C2×#179887822
C2×#179887302
C2×#179886872
C2×#179886592
C2×#179885862
C2×#179885812
C2×#553×C732
C2×#330973