Finite Group Databasebeta

← C2×#22620807 #33956664

Subgroups — C2×#22620807 #33956664

Order 18688.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989158C211yesmaximal, characteristic, complemented
2#22620807C2116yesmaximal, direct product factor
3C2×#17988922C211yesmaximal, characteristic, complemented
4C2×#17988925C211yesmaximal, characteristic, complemented
5C2×#17988908C211yesmaximal, characteristic, complemented
6C2×#17988917C211yesmaximal, characteristic, complemented
7C2×#17988843C211yesmaximal, characteristic, complemented
8C2×#17988831C211yesmaximal, characteristic, complemented
9C2×#17988826C211yesmaximal, characteristic, complemented
10C2×#17988814C211yesmaximal, characteristic, complemented
11C2×#17988749C211yesmaximal, characteristic, complemented
12C2×#17988749C211yesmaximal, characteristic, complemented
13C2×#17988742C211yesmaximal, characteristic, complemented
14C2×#17988725C211yesmaximal, characteristic, complemented
15C2×#17988554C211yesmaximal, characteristic, complemented
16C2×#537×C73C211yesmaximal, characteristic
17C23×Dic146C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21C22×#11924016C2211yescharacteristic
22C22×#11924012C2211yescharacteristic
23C23×#10596831C2211yescharacteristic
24#17989158—24no—
25#17989158C2218yescomplemented
26C2×#14556589—21no—
27C2×#14556578—21no—
28C2×#14556572—21no—
29C2×#14556572—21no—
30C2×#14556570C2211yescharacteristic
31C2×#14556570C2211yescharacteristic
32C2×#14556570C2211yescharacteristic
33C2×#14556570C2211yescharacteristic
34C2×#14556550C2211yescharacteristic
35#17988925C2218yescomplemented
36#17988922C2218yescomplemented
37#17988917C2218yescomplemented
38#17988908C2218yescomplemented
39#17988843C2218yescomplemented
40#17988831C2218yescomplemented
41#17988826C2218yescomplemented
42#17988814C2218yescomplemented
43#17988749C2218yescomplemented
44#17988749C2218yescomplemented
45#17988742C2218yescomplemented
46#17988725C2218yescomplemented
47C2×#14556524C2211yescharacteristic
48C2×#14556524C2211yescharacteristic
49C2×#14556522C2211yescharacteristic
50C2×#14556522C2211yescharacteristic
51C2×#14556515C2211yescharacteristic
52C2×#14556515C2211yescharacteristic
53C2×#14556514C2211yescharacteristic
54C2×#14556514C2211yescharacteristic
55C2×#14556514C2211yescharacteristic
56C2×#14556514C2211yescharacteristic
57C2×#14556512C2211yescharacteristic
58C2×#14556512C2211yescharacteristic
59#17988554C2218yescomplemented
60C2×C22⋊#10596831C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×C22⋊#10596831C2211yescharacteristic
63C2×C22⋊#10596831C2211yescharacteristic
64C22×#41×C73C2211yescharacteristic
65C22×#41×C73C2211yescharacteristic
66#537×C73—24no—
67#537×C73C2218yes—
68C2×C22⋊Q8×C73—21no—
69C2×C22⋊Q8×C73C2211yescharacteristic
70C2×C22⋊Q8×C73C2211yescharacteristic
71C2×#121×C73—21no—
72C2×#121×C73—21no—
73C2×#121×C73—21no—
74C2×#121×C73C2211yescharacteristic
75C2×#121×C73C2211yescharacteristic
76C22×C4⋊C4×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—22no—
79C22×Dic146—42no—
80C22×Dic146—42no—
81C22×Dic146C2311yescharacteristic
82C22×Dic146C2311yescharacteristic
83C22×Dic146C2314yes—
84C23×Dic73—21no—
85C2×#11924018—42no—
86C2×#11924018—42no—
87C2×#11924018C2314yes—
88C2×#11924018C2314yes—
89C2×#11924016—42no—
90C2×#11924016—42no—
91C2×#11924016C2314yes—
92C2×#11924016C2314yes—
93C2×#11924012—42no—
94C2×#11924012C2314yes—
95C22×#10596831—42no—
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99C22×#10596831C2311yescharacteristic
100C22×#10596831C2314yes—
101#14556589—28no—
102#14556578—28no—
103#14556572—28no—
104#14556572—28no—
105#14556570—22no—
106#14556570—22no—
107#14556570—22no—
108#14556570—22no—
109#14556570C2314yes—
110#14556570C2314yes—
111#14556570C2314yes—
112#14556570C2314yes—
113#14556550—22no—
114#14556550C2314yes—
115C2×C4⋊Dic73C2311yescharacteristic
116C2×C4⋊Dic73C2311yescharacteristic
117C2×#11924007—21no—
118C2×#11924007—21no—
119C2×#11924007—21no—
120C2×#11924007—21no—
121C2×C22⋊Dic73—21no—
122C2×C22⋊Dic73—21no—
123C2×C22⋊Dic73—21no—
124C2×C22⋊Dic73—21no—
125C2×C22⋊Dic73—21no—
126C2×C4×Dic73—21no—
127#14556524C2314yes—
128#14556524C2314yes—
129#14556522C2314yes—
130#14556522C2314yes—
131#14556515C2314yes—
132#14556515C2314yes—
133#14556514C2314yes—
134#14556514C2314yes—
135#14556514C2314yes—
136#14556514C2314yes—
137#14556512C2314yes—
138#14556512C2314yes—
139C22⋊#10596831C2314yes—
140C22⋊#10596831C2314yes—
141C22⋊#10596831C2314yes—
142C22⋊#10596831C2314yes—
143C2×#41×C73—22no—
144C2×#41×C73—42no—
145C2×#41×C73—42no—
146C2×#41×C73—42no—
147C2×#41×C73—42no—
148C2×#41×C73D414yes—
149C2×#41×C73C2314yes—
150C2×#41×C73C2314yes—
151C22×Q8×C73D411yescharacteristic
152C22×Q8×C73C2311yescharacteristic
153C22×D4×C73—21no—
154C22×D4×C73—21no—
155C22×D4×C73—21no—
156C22×D4×C73D411yescharacteristic
157C22×D4×C73D411yescharacteristic
158C22×D4×C73D411yescharacteristic
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73—21no—
161C23×C4×C73—21no—
162C23×C4×C73C2311yescharacteristic
163C23×C4×C73C2311yescharacteristic
164C23×C4×C73C2311yescharacteristic
165C22⋊Q8×C73—28no—
166C22⋊Q8×C73—22no—
167C22⋊Q8×C73—22no—
168C22⋊Q8×C73C2314yes—
169C22⋊Q8×C73C2314yes—
170#121×C73—28no—
171#121×C73—28no—
172#121×C73—28no—
173#121×C73—22no—
174#121×C73—22no—
175#121×C73C2314yes—
176#121×C73C2314yes—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73—22no—
179C2×C4⋊C4×C73—21no—
180C2×C4⋊C4×C73—21no—
181C2×C4⋊C4×C73C2311yescharacteristic
182C2×C4⋊C4×C73C2311yescharacteristic
183C2×C4⋊C4×C73C2314yes—
184C2×C22⋊C4×C73—21no—
185C2×C22⋊C4×C73—21no—
186C2×C22⋊C4×C73—21no—
187C2×C22⋊C4×C73—21no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—21no—
193C2×Dic146—21no—
194C2×Dic146—24no—
195C2×Dic146—44no—
196C2×Dic146—44no—
197C2×Dic146—44no—
198C2×Dic146—48no—
199C2×Dic146C2412yes—
200C2×Dic146C2412yes—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—24no—
206C22×Dic73—44no—
207#11924018—44no—
208#11924018—44no—
209#11924016—44no—
210#11924016—44no—
211#11924012—44no—
212C2×#10596831—22no—
213C2×#10596831—22no—
214C2×#10596831—22no—
215C2×#10596831—22no—
216C2×#10596831—44no—
217C2×#10596831C2412yes—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C2×#10596831C2412yes—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73C2412yes—
224C4⋊Dic73C2412yes—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231C22⋊Dic73—24no—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234C4×Dic73—24no—
235C24×C73—21no—
236C24×C73C2×D411yescharacteristic
237C24×C73C2×D411yescharacteristic
238C24×C73C2×D411yescharacteristic
239#41×C73—48no—
240#41×C73—44no—
241#41×C73—44no—
242#41×C73—44no—
243#41×C73—44no—
244#41×C73—48no—
245C2×Q8×C73—21no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73—42no—
249C2×Q8×C73C2×D414yes—
250C2×Q8×C73C2412yes—
251C2×D4×C73—24no—
252C2×D4×C73—24no—
253C2×D4×C73—24no—
254C2×D4×C73—21no—
255C2×D4×C73—22no—
256C2×D4×C73—22no—
257C2×D4×C73—42no—
258C2×D4×C73—42no—
259C2×D4×C73—42no—
260C2×D4×C73—44no—
261C2×D4×C73—82no—
262C2×D4×C73—82no—
263C2×D4×C73C2×D414yes—
264C2×D4×C73C2×D414yes—
265C2×D4×C73C2×D414yes—
266C2×D4×C73C2412yes—
267C22×C4×C73—22no—
268C22×C4×C73—22no—
269C22×C4×C73—22no—
270C22×C4×C73—22no—
271C22×C4×C73—22no—
272C22×C4×C73—22no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—24no—
277C22×C4×C73—24no—
278C22×C4×C73—44no—
279C22×C4×C73—82no—
280C22×C4×C73C2×D411yescharacteristic
281C22×C4×C73C2×D411yescharacteristic
282C22×C4×C73C2×D411yescharacteristic
283C22×C4×C73C2×D412yes—
284C22×C4×C73C2×D412yes—
285C22×C4×C73C2×D412yes—
286C22×C4×C73C2412yes—
287C22×C4×C73C2412yes—
288C22×C4×C73C2412yes—
289C22×C4×C73C2411yescharacteristic
290C4⋊C4×C73—24no—
291C4⋊C4×C73—21no—
292C4⋊C4×C73—21no—
293C4⋊C4×C73—24no—
294C4⋊C4×C73—24no—
295C4⋊C4×C73C2412yes—
296C4⋊C4×C73C2412yes—
297C22⋊C4×C73—24no—
298C22⋊C4×C73—24no—
299C22⋊C4×C73—24no—
300C22⋊C4×C73—24no—
301C23×C73—22no—
302C23×C73—22no—
303C23×C73—22no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73—22no—
309C23×C73—22no—
310C23×C73—22no—
311C23×C73—42no—
312C23×C73—42no—
313C23×C73—42no—
314C23×C73C22×D412yes—
315C23×C73C22×D412yes—
316C23×C73C22×D412yes—
317C23×C73C22×D411yescharacteristic
318Q8×C73—22no—
319Q8×C73—22no—
320Q8×C73—44no—
321Q8×C73—42no—
322D4×C73—22no—
323D4×C73—22no—
324D4×C73—44no—
325D4×C73—44no—
326D4×C73—44no—
327D4×C73—48no—
328D4×C73—42no—
329D4×C73—84no—
330D4×C73—84no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—24no—
335C2×C4×C73—24no—
336C2×C4×C73—24no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—48no—
347C2×C4×C73—42no—
348C2×C4×C73—42no—
349C2×C4×C73—42no—
350C2×C4×C73—84no—
351C2×C4×C73C22×D412yes—
352C2×C4×C73C22×D412yes—
353C2×C4×C73C22×D412yes—
354C2×C4×C73C22×D411yescharacteristic
355C2×C4×C73H(5,𝔽2)12yes—
356C2×C4×C73H(5,𝔽2)12yes—
357C2×C4×C73C2511yescharacteristic
358C2×Dic73—22no—
359C2×Dic73—22no—
360C2×Dic73—22no—
361C2×Dic73—22no—
362C2×Dic73—48no—
363C2×Dic73—42no—
364C2×Dic73—42no—
365C2×Dic73—42no—
366C2×Dic73—42no—
367Dic146—22no—
368Dic146—22no—
369Dic146—22no—
370Dic146—22no—
371Dic146—48no—
372Dic146—42no—
373Dic146—42no—
374#10596831—22no—
375#10596831—22no—
376#10596831—22no—
377#10596831—22no—
378C22×C73—22no—
379C22×C73—22no—
380C22×C73—22no—
381C22×C73—22no—
382C22×C73—22no—
383C22×C73—22no—
384C22×C73—22no—
385C22×C73—22no—
386C22×C73—22no—
387C22×C73—44no—
388C22×C73—44no—
389C22×C73—44no—
390C22×C73—42no—
391C22×C73—42no—
392C22×C73—42no—
393C22×C73—84no—
394C22×C73#53412yes—
395C22×C73#57712yes—
396C22×C73#57812yes—
397C22×C73C23×D411yescharacteristic
398C4×C73—22no—
399C4×C73—22no—
400C4×C73—22no—
401C4×C73—42no—
402C4×C73—42no—
403C4×C73—42no—
404C4×C73#53412yes—
405C4×C73C2×H(5,𝔽2)11yescharacteristic
406C4×C73C2×H(5,𝔽2)11yescharacteristic
407Dic73—42no—
408Dic73—42no—
409Dic73—42no—
410Dic73—42no—
411C2×#3201—731nomaximal, Sylow
412C2×C73—42no—
413C2×C73—42no—
414C2×C73—42no—
415C2×C73—82no—
416C2×C73#320114yescomplemented
417C2×C73C2×#53411yescharacteristic
418C2×C73C2×#57711yescharacteristic
419C2×C73C2×#57811yescharacteristic
420C2×#537D7311yescharacteristic
421C2×#536—731no—
422#3201—7316no—
423C2×#484—731no—
424C2×#485—731no—
425C2×#482—731no—
426C2×#483—731no—
427C2×#470—731no—
428C2×#468—731no—
429C2×#467—731no—
430C2×#465—731no—
431C2×#452—731no—
432C2×#452—731no—
433C2×#451—731no—
434C2×#448—731no—
435C2×#408—731no—
436C73C2×#320111yescharacteristic, complemented, Sylow
437C22×#41C2×D7311yescharacteristic
438C22×#41C2×D7311yescharacteristic
439C23×Q8—731no—
440C22×Q16—731no—
441C22×Q16—731no—
442C22×SD16—731no—
443C22×SD16—731no—
444C22×M16—731no—
445C23×C8—731no—
446#537—24no—
447#537C2×D7318yes—
448#536—738no—
449#536—1464no—
450C2×C4⋊Q8—1461no—
451C2×#124—1461no—
452C2×#123—1461no—
453C2×#123—1461no—
454C2×C22⋊Q8—21no—
455C2×C22⋊Q8—731no—
456C2×C22⋊Q8—731no—
457C2×C22⋊Q8—731no—
458C2×C22⋊Q8—731no—
459C2×C22⋊Q8C2×D7311yescharacteristic
460C2×C22⋊Q8C2×D7311yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C2×D7311yescharacteristic
465C2×#121C2×D7311yescharacteristic
466C2×#117—731no—
467C22×C4⋊C4C2×D7311yescharacteristic
468#485—738no—
469#484—738no—
470#483—738no—
471#482—738no—
472#470—738no—
473#468—738no—
474#467—738no—
475#465—738no—
476#452—738no—
477#452—738no—
478#451—738no—
479#448—738no—
480C2×#107—731no—
481C2×#107—731no—
482C2×#106—731no—
483C2×#106—731no—
484C2×#103—731no—
485C2×#103—731no—
486C2×#103—731no—
487C2×#103—731no—
488C2×#103—731no—
489C2×#103—731no—
490C2×#102—731no—
491C2×#102—731no—
492#408—738no—
493C2×C22⋊C8—731no—
494C2×C22⋊C8—731no—
495C2×C22⋊C8—731no—
496C2×C22⋊C8—731no—
497C2×#41—22no—
498C2×#41—42no—
499C2×#41—42no—
500C2×#41—42no—
501C2×#41—42no—
502C2×#41C22⋊D7314yes—
503C2×#41C22×D7314yes—
504C2×#41C22×D7314yes—
505C22×Q8—2922no—
506C22×Q8—2922no—
507C22×Q8—734no—
508C22×Q8—731no—
509C22×Q8—731no—
510C22×Q8—1461no—
511C22×Q8—1462no—
512C22×Q8C22⋊D7311yescharacteristic
513C22×Q8C22×D7311yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4C22⋊D7311yescharacteristic
518C22×D4C22⋊D7311yescharacteristic
519C22×D4C22⋊D7311yescharacteristic
520C22×D4C22×D7311yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—1461no—
524C23×C4C22×D7311yescharacteristic
525C23×C4C22×D7311yescharacteristic
526C23×C4C22×D7311yescharacteristic
527C2×Q16—2922no—
528C2×Q16—2922no—
529C2×Q16—734no—
530C2×Q16—734no—
531C2×SD16—2922no—
532C2×SD16—2922no—
533C2×SD16—734no—
534C2×SD16—734no—
535C2×M16—2922no—
536C2×M16—734no—
537C22×C8—2922no—
538C22×C8—734no—
539C22×C8—731no—
540C22×C8—731no—
541C22×C8—731no—
542C22×C8—731no—
543C4⋊Q8—1468no—
544#124—1468no—
545#123—1468no—
546#123—1468no—
547C22⋊Q8—28no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—734no—
551C22⋊Q8—734no—
552C22⋊Q8—734no—
553C22⋊Q8—734no—
554C22⋊Q8—1462no—
555C22⋊Q8—1462no—
556C22⋊Q8—1462no—
557C22⋊Q8—1462no—
558C22⋊Q8C22×D7314yes—
559C22⋊Q8C22×D7314yes—
560#121—28no—
561#121—28no—
562#121—28no—
563#121—22no—
564#121—22no—
565#121C22×D7314yes—
566#121C22×D7314yes—
567#117—734no—
568#117—1462no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—731no—
574C2×C4⋊C4—731no—
575C2×C4⋊C4—1461no—
576C2×C4⋊C4—1461no—
577C2×C4⋊C4—1461no—
578C2×C4⋊C4—1461no—
579C2×C4⋊C4C22×D7311yescharacteristic
580C2×C4⋊C4C22×D7311yescharacteristic
581C2×C4⋊C4C22×D7314yes—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—1461no—
587C2×C22⋊C4—1461no—
588C2×C22⋊C4—1461no—
589C2×C22⋊C4—1461no—
590C2×C22⋊C4—1461no—
591C2×C42—1461no—
592#107—734no—
593#107—734no—
594#106—734no—
595#106—734no—
596#103—734no—
597#103—734no—
598#103—734no—
599#103—734no—
600#103—734no—
601#103—734no—
602#102—734no—
603#102—734no—
604C22⋊C8—734no—
605C22⋊C8—734no—
606C22⋊C8—734no—
607C22⋊C8—734no—
608C24—21no—
609C24C2×C22⋊D7311yescharacteristic
610C24C2×C22⋊D7311yescharacteristic
611C24C2×C22⋊D7311yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—44no—
616#41—44no—
617#41—48no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—42no—
622C2×Q8—2924no—
623C2×Q8—2928no—
624C2×Q8—2924no—
625C2×Q8—2924no—
626C2×Q8—732no—
627C2×Q8—732no—
628C2×Q8—1462no—
629C2×Q8—1462no—
630C2×Q8—1462no—
631C2×Q8—1462no—
632C2×Q8—1461no—
633C2×Q8—1461no—
634C2×Q8—1464no—
635C2×Q8C2×C22⋊D7314yes—
636C2×Q8C23×D7312yes—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—82no—
649C2×D4C2×C22⋊D7314yes—
650C2×D4C2×C22⋊D7314yes—
651C2×D4C2×C22⋊D7314yes—
652C2×D4C23×D7312yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—44no—
665C22×C4—82no—
666C22×C4—2924no—
667C22×C4—1464no—
668C22×C4—1461no—
669C22×C4—1461no—
670C22×C4—1461no—
671C22×C4—1461no—
672C22×C4C2×C22⋊D7312yes—
673C22×C4C2×C22⋊D7312yes—
674C22×C4C2×C22⋊D7312yes—
675C22×C4C2×C22⋊D7311yescharacteristic
676C22×C4C2×C22⋊D7311yescharacteristic
677C22×C4C2×C22⋊D7311yescharacteristic
678C22×C4C23×D7312yes—
679C22×C4C23×D7312yes—
680C22×C4C23×D7312yes—
681C22×C4C23×D7311yescharacteristic
682Q16—2924no—
683Q16—2924no—
684SD16—2924no—
685SD16—2924no—
686M16—2924no—
687C2×C8—2924no—
688C2×C8—732no—
689C2×C8—732no—
690C2×C8—732no—
691C2×C8—732no—
692C2×C8—1462no—
693C2×C8—1462no—
694C2×C8—1462no—
695C2×C8—1462no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—732no—
702C4⋊C4—732no—
703C4⋊C4—1464no—
704C4⋊C4—1464no—
705C4⋊C4—1464no—
706C4⋊C4—1464no—
707C4⋊C4—1461no—
708C4⋊C4—1461no—
709C4⋊C4C23×D7312yes—
710C4⋊C4C23×D7312yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—1464no—
716C22⋊C4—1464no—
717C22⋊C4—1464no—
718C22⋊C4—1464no—
719C22⋊C4—1464no—
720C42—1464no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23C22×C22⋊D7312yes—
735C23C22×C22⋊D7312yes—
736C23C22×C22⋊D7312yes—
737C23C22×C22⋊D7311yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—44no—
741Q8—42no—
742Q8—2928no—
743Q8—2922no—
744Q8—2922no—
745Q8—1462no—
746Q8—1462no—
747Q8—1462no—
748Q8—1462no—
749D4—22no—
750D4—22no—
751D4—44no—
752D4—44no—
753D4—44no—
754D4—48no—
755D4—42no—
756D4—84no—
757D4—84no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—84no—
778C2×C4—2928no—
779C2×C4—2922no—
780C2×C4—2922no—
781C2×C4—2922no—
782C2×C4—2922no—
783C2×C4—1462no—
784C2×C4—1462no—
785C2×C4—1462no—
786C2×C4—1462no—
787C2×C4C22×C22⋊D7312yes—
788C2×C4C22×C22⋊D7312yes—
789C2×C4C22×C22⋊D7312yes—
790C2×C4C22×C22⋊D7311yescharacteristic
791C2×C4#1455663612yes—
792C2×C4#1455663612yes—
793C2×C4C24×D7311yescharacteristic
794C8—1462no—
795C8—1462no—
796C8—1462no—
797C8—1462no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—84no—
814C22#1798914612yes—
815C22#1798939812yes—
816C22#1798940212yes—
817C22C23×C22⋊D7311yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—2922no—
825C4—2922no—
826C4—2922no—
827C4—2922no—
828C4#1798914612yes—
829C4C2×#1455663611yescharacteristic
830C4C2×#1455663611yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—82no—
835C2#2262080714yesdirect product factor
836C2C2×#1798914611yescharacteristic
837C2C2×#1798939811yescharacteristic
838C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
Fitting, prime radicalC2×#537×C73C2
socleC23×C73C22×D4
hypercenterC2×#537D73
hypocenterC73C2×#3201
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#17989158C2semidirect
2. #22620807C2direct (N × H)
3. C2×#17988922C2semidirect
4. C2×#17988925C2semidirect
5. C2×#17988908C2semidirect
6. C2×#17988917C2semidirect
7. C2×#17988843C2semidirect
8. C2×#17988831C2semidirect
9. C2×#17988826C2semidirect
10. C2×#17988814C2semidirect
11. C2×#17988749C2semidirect
12. C2×#17988749C2semidirect
13. C2×#17988742C2semidirect
14. C2×#17988725C2semidirect
15. C2×#17988554C2semidirect
25. #17989158C22semidirect
35. #17988925C22semidirect
36. #17988922C22semidirect
37. #17988917C22semidirect
38. #17988908C22semidirect
39. #17988843C22semidirect
40. #17988831C22semidirect
41. #17988826C22semidirect
42. #17988814C22semidirect
43. #17988749C22semidirect
44. #17988749C22semidirect
45. #17988742C22semidirect
46. #17988725C22semidirect
59. #17988554C22semidirect
416. C2×C73#3201semidirect
436. C73C2×#3201semidirect
835. C2#22620807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891582
#226208072
C2×#179889222
C2×#179889252
C2×#179889082
C2×#179889172
C2×#179888432
C2×#179888312
C2×#179888262
C2×#179888142
C2×#179887492
C2×#179887422
C2×#179887252
C2×#179885542
C2×#537×C732
C2×#320173