Finite Group Databasebeta

← C2×#22615050 #33256124

Subgroups — C2×#22615050 #33256124

Order 18688.

2834 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
1C22×#14556581C211yesmaximal, characteristic, complemented
2C22×#14556572C211yesmaximal, characteristic
3#22615050C2116yesmaximal, direct product factor
4C2×#17988525C211yesmaximal, characteristic, complemented
5C2×#17988510C211yesmaximal, characteristic, complemented
6C2×#17988510C211yesmaximal, characteristic, complemented
7C2×#17988501C211yesmaximal, characteristic
8C2×#17988485C211yesmaximal, characteristic, complemented
9C2×#17988480C211yesmaximal, characteristic, complemented
10C2×#17988480C211yesmaximal, characteristic, complemented
11C2×#17988475C211yesmaximal, characteristic, complemented
12C2×#17988475C211yesmaximal, characteristic, complemented
13C2×#17988462C211yesmaximal, characteristic, complemented
14C2×C4×#11924007C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
16C2×#390×C73C211yesmaximal, characteristic
17C24×Dic73C2211yescharacteristic
18C2×#14556581—28no—
19C2×#14556581C2218yescomplemented
20C2×#14556572—28no—
21C2×#14556572C2218yes—
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C4⋊Dic73C2211yescharacteristic
24C22×C4⋊Dic73C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×C22⋊Dic73C2211yescharacteristic
32C22×C22⋊Dic73C2211yescharacteristic
33C22×C22⋊Dic73C2211yescharacteristic
34C22×C22⋊Dic73C2211yescharacteristic
35C22×C22⋊Dic73C2211yescharacteristic
36C22×C22⋊Dic73C2211yescharacteristic
37C22×C22⋊Dic73C2211yescharacteristic
38C22×C4×Dic73C2211yescharacteristic
39C22×C4×Dic73C2211yescharacteristic
40C22×C4×Dic73C2211yescharacteristic
41#17988525C2218yescomplemented
42#17988510C2218yescomplemented
43#17988510C2218yescomplemented
44#17988501C2218yes—
45#17988485C2218yescomplemented
46#17988480C2218yescomplemented
47#17988480C2218yescomplemented
48#17988475C2218yescomplemented
49#17988475C2218yescomplemented
50#17988462C2218yescomplemented
51C4×#11924007C2218yescomplemented
52C22⋊C4×Dic73C2218yescomplemented
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C23×D4×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×C22⋊C4×C73C2211yescharacteristic
64C22×C22⋊C4×C73C2211yescharacteristic
65C22×C22⋊C4×C73C2211yescharacteristic
66C22×C22⋊C4×C73C2211yescharacteristic
67C22×C42×C73C2211yescharacteristic
68#390×C73C2218yes—
69C23×Dic73—24no—
70C23×Dic73—24no—
71C23×Dic73—42no—
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2314yes—
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81#14556581—232no—
82#14556572—232no—
83C2×C4⋊Dic73—24no—
84C2×C4⋊Dic73—24no—
85C2×C4⋊Dic73—42no—
86C2×C4⋊Dic73C2314yes—
87C2×C4⋊Dic73C2314yes—
88C2×C4⋊Dic73C2314yes—
89C2×#11924007—24no—
90C2×#11924007—24no—
91C2×#11924007—24no—
92C2×#11924007—24no—
93C2×#11924007—24no—
94C2×#11924007D418yes—
95C2×#11924007C2314yes—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×C22⋊Dic73—24no—
102C2×C22⋊Dic73—24no—
103C2×C22⋊Dic73—24no—
104C2×C22⋊Dic73—24no—
105C2×C22⋊Dic73—24no—
106C2×C22⋊Dic73—24no—
107C2×C22⋊Dic73—42no—
108C2×C22⋊Dic73C2314yes—
109C2×C22⋊Dic73C2314yes—
110C2×C22⋊Dic73C2314yes—
111C2×C22⋊Dic73C2314yes—
112C2×C22⋊Dic73C2314yes—
113C2×C22⋊Dic73C2314yes—
114C2×C22⋊Dic73C2314yes—
115C2×C4×Dic73—24no—
116C2×C4×Dic73—24no—
117C2×C4×Dic73—42no—
118C2×C4×Dic73C2314yes—
119C2×C4×Dic73C2314yes—
120C2×C4×Dic73C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129C25×C73C2311yescharacteristic
130C25×C73C2311yescharacteristic
131C22×D4×C73—24no—
132C22×D4×C73—24no—
133C22×D4×C73—42no—
134C22×D4×C73C2314yes—
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C23×C4×C73C2311yescharacteristic
139C23×C4×C73C2311yescharacteristic
140C2×C4⋊C4×C73—24no—
141C2×C4⋊C4×C73C2314yes—
142C2×C22⋊C4×C73—24no—
143C2×C22⋊C4×C73—24no—
144C2×C22⋊C4×C73—24no—
145C2×C22⋊C4×C73—24no—
146C2×C22⋊C4×C73C2314yes—
147C2×C22⋊C4×C73C2314yes—
148C2×C22⋊C4×C73C2314yes—
149C2×C22⋊C4×C73C2314yes—
150C2×C42×C73—42no—
151C2×C42×C73C2314yes—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—22no—
155C22×Dic73—22no—
156C22×Dic73—22no—
157C22×Dic73—22no—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—28no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—28no—
175C22×Dic73—44no—
176C22×Dic73—416no—
177C22×Dic73C2×D414yes—
178C22×Dic73C2×D414yes—
179C22×Dic73#4114yes—
180C22×Dic73C2412yes—
181C22×Dic73C2412yes—
182C22×Dic73C2412yes—
183C22×Dic73C2412yes—
184C22×Dic73C2412yes—
185C22×Dic73C2412yes—
186C22×Dic73C2412yes—
187C22×Dic73C2412yes—
188C4⋊Dic73—28no—
189C4⋊Dic73—28no—
190C4⋊Dic73—44no—
191#11924007—28no—
192#11924007—28no—
193#11924007—28no—
194#11924007—28no—
195#11924007—28no—
196#11924007C2×D4116yes—
197C22⋊Dic73—28no—
198C22⋊Dic73—28no—
199C22⋊Dic73—28no—
200C22⋊Dic73—28no—
201C22⋊Dic73—28no—
202C22⋊Dic73—28no—
203C22⋊Dic73—44no—
204C4×Dic73—28no—
205C4×Dic73—28no—
206C4×Dic73—44no—
207C24×C73—22no—
208C24×C73—22no—
209C24×C73—22no—
210C24×C73—22no—
211C24×C73—22no—
212C24×C73—22no—
213C24×C73—22no—
214C24×C73—22no—
215C24×C73—22no—
216C24×C73—22no—
217C24×C73—22no—
218C24×C73—22no—
219C24×C73—22no—
220C24×C73#4114yes—
221C24×C73C2412yes—
222C24×C73C2412yes—
223C24×C73C2411yescharacteristic
224C2×D4×C73—28no—
225C2×D4×C73—28no—
226C2×D4×C73—44no—
227C2×D4×C73—416no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—22no—
233C22×C4×C73—22no—
234C22×C4×C73—22no—
235C22×C4×C73—22no—
236C22×C4×C73—22no—
237C22×C4×C73—22no—
238C22×C4×C73—22no—
239C22×C4×C73—22no—
240C22×C4×C73C2×D414yes—
241C22×C4×C73#4114yes—
242C22×C4×C73#4114yes—
243C22×C4×C73C2412yes—
244C22×C4×C73C2412yes—
245C22×C4×C73C2412yes—
246C22×C4×C73C2412yes—
247C22×C4×C73C2412yes—
248C4⋊C4×C73—28no—
249C22⋊C4×C73—28no—
250C22⋊C4×C73—28no—
251C22⋊C4×C73—28no—
252C22⋊C4×C73—28no—
253C42×C73—44no—
254C23×C73—28no—
255C23×C73—28no—
256C23×C73—28no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—22no—
260C23×C73—22no—
261C23×C73—22no—
262C23×C73—22no—
263C23×C73—22no—
264C23×C73—22no—
265C23×C73—22no—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73—44no—
271C23×C73—44no—
272C23×C73—44no—
273C23×C73—44no—
274C23×C73—44no—
275C23×C73—44no—
276C23×C73—44no—
277C23×C73—44no—
278C23×C73—44no—
279C23×C73—44no—
280C23×C73—44no—
281C23×C73C22×D412yes—
282C23×C73C2×#4112yes—
283C23×C73C2×#4112yes—
284C23×C73C2×#4112yes—
285C23×C73C2×#4114yes—
286C23×C73C2×#4112yes—
287C23×C73H(5,𝔽2)12yes—
288C23×C732−1+412yes—
289C23×C73C2511yescharacteristic
290D4×C73—416no—
291C2×C4×C73—28no—
292C2×C4×C73—28no—
293C2×C4×C73—28no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—44no—
307C2×C4×C73—44no—
308C2×C4×C73C22×D414yes—
309C2×C4×C73C2×#4114yes—
310C2×C4×C73C2×#4114yes—
311C2×Dic73—28no—
312C2×Dic73—28no—
313C2×Dic73—28no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—416no—
336C2×Dic73—44no—
337C2×Dic73—44no—
338C2×Dic73—44no—
339C2×Dic73—44no—
340C2×Dic73—44no—
341C2×Dic73C22×D414yes—
342C2×Dic73C22×D414yes—
343C2×Dic73C2×#4114yes—
344C22×C73—24no—
345C22×C73—24no—
346C22×C73—24no—
347C22×C73—42no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—416no—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—42no—
358C22×C73—42no—
359C22×C73—88no—
360C22×C73#52914yes—
361C22×C73#53214yes—
362C22×C73#53914yes—
363C22×C73#54614yes—
364C22×C73#54814yes—
365C22×C73#55214yes—
366C22×C73#55314yes—
367C22×C73C23×D411yescharacteristic
368C22×C73C22×#4111yescharacteristic
369C22×C73C22×#4111yescharacteristic
370C22×C73C22×#4111yescharacteristic
371C22×C73C22×#4111yescharacteristic
372C22×C73C2×H(5,𝔽2)11yescharacteristic
373C22×C73C2×2−1+411yescharacteristic
374C4×C73—24no—
375C4×C73—24no—
376C4×C73—24no—
377C4×C73—42no—
378C4×C73—42no—
379Dic73—24no—
380Dic73—24no—
381Dic73—24no—
382Dic73—42no—
383Dic73—42no—
384Dic73—42no—
385Dic73—42no—
386Dic73—42no—
387C2×#2558—731nomaximal, Sylow
388C2×C73—44no—
389C2×C73—82no—
390C2×C73#255818yescomplemented
391C2×C73C2×#52911yescharacteristic
392C2×C73C2×#53211yescharacteristic
393C2×C73C2×#53911yescharacteristic
394C2×C73C2×#54611yescharacteristic
395C2×C73C2×#54811yescharacteristic
396C2×C73C2×#55211yescharacteristic
397C2×C73C2×#55311yescharacteristic
398C22×#125—731no—
399C22×#123—731no—
400#2558—7316no—
401C2×#400—731no—
402C2×#396—731no—
403C2×#396—731no—
404C2×#394—731no—
405C2×#390D7311yescharacteristic
406C2×#389—731no—
407C2×#388—731no—
408C2×#388—731no—
409C2×#388—731no—
410C2×#388—731no—
411C2×#385—731no—
412C2×C4×C4⋊C4—731no—
413C2×C4×C22⋊C4—731no—
414C73C2×#255811yescharacteristic, complemented, Sylow
415C23×D4C2×D7311yescharacteristic
416C24×C4—731no—
417C2×#125—738no—
418C2×#125—1468no—
419C2×#123—738no—
420C2×#123—1468no—
421C22×C4⋊C4—731no—
422C22×C4⋊C4—731no—
423C22×C4⋊C4—731no—
424C22×C4⋊C4—731no—
425C22×C4⋊C4—731no—
426C22×C4⋊C4—731no—
427C22×C4⋊C4—731no—
428C22×C4⋊C4—731no—
429C22×C4⋊C4—731no—
430C22×C4⋊C4C2×D7311yescharacteristic
431C22×C22⋊C4—731no—
432C22×C22⋊C4—731no—
433C22×C22⋊C4—731no—
434C22×C22⋊C4—731no—
435C22×C22⋊C4—731no—
436C22×C22⋊C4—731no—
437C22×C22⋊C4—731no—
438C22×C22⋊C4C2×D7311yescharacteristic
439C22×C22⋊C4C2×D7311yescharacteristic
440C22×C22⋊C4C2×D7311yescharacteristic
441C22×C22⋊C4C2×D7311yescharacteristic
442C22×C42—731no—
443C22×C42—731no—
444C22×C42—731no—
445C22×C42C2×D7311yescharacteristic
446#400—738no—
447#396—738no—
448#396—738no—
449#394—738no—
450#390C2×D7318yes—
451#389—738no—
452#388—738no—
453#388—738no—
454#388—738no—
455#388—738no—
456#385—738no—
457C4×C4⋊C4—738no—
458C4×C22⋊C4—738no—
459C2×#95—731no—
460C2×#95—731no—
461C2×#95—731no—
462C2×#95—731no—
463C2×#95—731no—
464C2×#95—731no—
465C2×#95—731no—
466C2×#95—731no—
467C25C22×D7311yescharacteristic
468C25C22×D7311yescharacteristic
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—42no—
472C22×D4C22×D7314yes—
473C23×C4—2922no—
474C23×C4—734no—
475C23×C4—731no—
476C23×C4—731no—
477C23×C4—731no—
478C23×C4—731no—
479C23×C4—731no—
480C23×C4—731no—
481C23×C4—731no—
482C23×C4—731no—
483C23×C4—1464no—
484C23×C4—1464no—
485C23×C4C22×D7311yescharacteristic
486C23×C4C22×D7311yescharacteristic
487C23×C4C22×D7311yescharacteristic
488C23×C4C22×D7311yescharacteristic
489C23×C4C22×D7311yescharacteristic
490#125—14632no—
491#123—14632no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—2922no—
494C2×C4⋊C4—734no—
495C2×C4⋊C4—738no—
496C2×C4⋊C4—734no—
497C2×C4⋊C4—734no—
498C2×C4⋊C4—734no—
499C2×C4⋊C4—734no—
500C2×C4⋊C4—734no—
501C2×C4⋊C4—734no—
502C2×C4⋊C4—734no—
503C2×C4⋊C4—734no—
504C2×C4⋊C4—1464no—
505C2×C4⋊C4—1464no—
506C2×C4⋊C4—1464no—
507C2×C4⋊C4—1464no—
508C2×C4⋊C4—1464no—
509C2×C4⋊C4—1464no—
510C2×C4⋊C4—1464no—
511C2×C4⋊C4C22×D7314yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—2922no—
517C2×C22⋊C4—734no—
518C2×C22⋊C4—734no—
519C2×C22⋊C4—734no—
520C2×C22⋊C4—734no—
521C2×C22⋊C4—734no—
522C2×C22⋊C4—734no—
523C2×C22⋊C4—734no—
524C2×C22⋊C4—1464no—
525C2×C22⋊C4—1464no—
526C2×C22⋊C4—1464no—
527C2×C22⋊C4—1464no—
528C2×C22⋊C4—1464no—
529C2×C22⋊C4—1464no—
530C2×C22⋊C4C22×D7314yes—
531C2×C22⋊C4C22×D7314yes—
532C2×C22⋊C4C22×D7314yes—
533C2×C22⋊C4C22×D7314yes—
534C2×C42—42no—
535C2×C42—2922no—
536C2×C42—734no—
537C2×C42—734no—
538C2×C42—734no—
539C2×C42—1464no—
540C2×C42—1464no—
541C2×C42C22×D7314yes—
542#95—734no—
543#95—734no—
544#95—734no—
545#95—734no—
546#95—734no—
547#95—734no—
548#95—734no—
549#95—734no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24#1192402814yes—
564C24C23×D7312yes—
565C24C23×D7312yes—
566C24C23×D7311yescharacteristic
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—44no—
570C2×D4—416no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—29216no—
584C22×C4—2924no—
585C22×C4—734no—
586C22×C4—734no—
587C22×C4—734no—
588C22×C4—732no—
589C22×C4—732no—
590C22×C4—732no—
591C22×C4—732no—
592C22×C4—732no—
593C22×C4—732no—
594C22×C4—732no—
595C22×C4—732no—
596C22×C4—1468no—
597C22×C4—1462no—
598C22×C4—1462no—
599C22×C4—1462no—
600C22×C4—1462no—
601C22×C4—1462no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4—1462no—
605C22×C4—1462no—
606C22×C4—1462no—
607C22×C4—1462no—
608C22×C4—1468no—
609C22×C4—1462no—
610C22×C4—1462no—
611C22×C4—1462no—
612C22×C4—1462no—
613C22×C4—1462no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1462no—
619C22×C4D4×D7314yes—
620C22×C4#1192402714yes—
621C22×C4#1192402714yes—
622C22×C4C23×D7312yes—
623C22×C4C23×D7312yes—
624C22×C4C23×D7312yes—
625C22×C4C23×D7312yes—
626C22×C4C23×D7312yes—
627C4⋊C4—28no—
628C4⋊C4—2924no—
629C4⋊C4—7316no—
630C4⋊C4—1468no—
631C4⋊C4—1468no—
632C4⋊C4—1468no—
633C4⋊C4—1468no—
634C4⋊C4—1468no—
635C4⋊C4—1468no—
636C4⋊C4—1468no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—2924no—
642C22⋊C4—1468no—
643C22⋊C4—1468no—
644C22⋊C4—1468no—
645C22⋊C4—1468no—
646C22⋊C4—1468no—
647C22⋊C4—1468no—
648C42—44no—
649C42—2924no—
650C42—1468no—
651C42—1468no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23C2×D4×D7312yes—
680C23#41×D7312yes—
681C23C2×#1192402712yes—
682C23C2×#1192402712yes—
683C23C2×#1192402814yes—
684C23C2×#1192402812yes—
685C23#1455663612yes—
686C23#1455663812yes—
687C23C24×D7311yescharacteristic
688D4—416no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—2924no—
707C2×C4—2924no—
708C2×C4—2924no—
709C2×C4—2924no—
710C2×C4—2924no—
711C2×C4—29216no—
712C2×C4—734no—
713C2×C4—734no—
714C2×C4—734no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1468no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1468no—
738C2×C4—1468no—
739C2×C4C2×D4×D7314yes—
740C2×C4C2×#1192402714yes—
741C2×C4C2×#1192402714yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—88no—
758C22#1798911714yes—
759C22#1798913514yes—
760C22#1798918214yes—
761C22#1798922714yes—
762C22#1798924514yes—
763C22#1798927714yes—
764C22#1798928014yes—
765C22C22×D4×D7311yescharacteristic
766C22C2×#41×D7311yescharacteristic
767C22C22×#1192402711yescharacteristic
768C22C22×#1192402711yescharacteristic
769C22C22×#1192402811yescharacteristic
770C22C2×#1455663611yescharacteristic
771C22C2×#1455663811yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—2922no—
778C4—2922no—
779C4—2922no—
780C4—2922no—
781C4—2922no—
782C4—1464no—
783C4—1464no—
784C4—1464no—
785C2—44no—
786C2—82no—
787C2#2261505018yesdirect product factor
788C2C2×#1798911711yescharacteristic
789C2C2×#1798913511yescharacteristic
790C2C2×#1798918211yescharacteristic
791C2C2×#1798922711yescharacteristic
792C2C2×#1798924511yescharacteristic
793C2C2×#1798927711yescharacteristic
794C2C2×#1798928011yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#390×C73C2
socleC24×C73C24
prime radicalC23×D4×C73C22
hypercenterC2×#390D73
hypocenterC73C2×#2558
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#14556581C2semidirect
3. #22615050C2direct (N × H)
4. C2×#17988525C2semidirect
5. C2×#17988510C2semidirect
6. C2×#17988510C2semidirect
8. C2×#17988485C2semidirect
9. C2×#17988480C2semidirect
10. C2×#17988480C2semidirect
11. C2×#17988475C2semidirect
12. C2×#17988475C2semidirect
13. C2×#17988462C2semidirect
14. C2×C4×#11924007C2semidirect
15. C2×C22⋊C4×Dic73C2semidirect
19. C2×#14556581C22semidirect
41. #17988525C22semidirect
42. #17988510C22semidirect
43. #17988510C22semidirect
45. #17988485C22semidirect
46. #17988480C22semidirect
47. #17988480C22semidirect
48. #17988475C22semidirect
49. #17988475C22semidirect
50. #17988462C22semidirect
51. C4×#11924007C22semidirect
52. C22⋊C4×Dic73C22semidirect
390. C2×C73#2558semidirect
414. C73C2×#2558semidirect
787. C2#22615050direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565812
C22×#145565722
#226150502
C2×#179885252
C2×#179885102
C2×#179885012
C2×#179884852
C2×#179884802
C2×#179884752
C2×#179884622
C2×C4×#119240072
C2×C22⋊C4×Dic732
C2×#390×C732
C2×#255873