Finite Group Databasebeta

← C2×#22614372 #33255756

Subgroups — C2×#22614372 #33255756

Order 18688.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556576C211yesmaximal, characteristic
2C22×#14556548C211yesmaximal, characteristic, complemented
3#22614372C2116yesmaximal, direct product factor
4C2×#17988528C211yesmaximal, characteristic, complemented
5C2×#17988522C211yesmaximal, characteristic, complemented
6C2×#17988521C211yesmaximal, characteristic, complemented
7C2×#17988516C211yesmaximal, characteristic, complemented
8C2×#17988479C211yesmaximal, characteristic, complemented
9C2×#17988478C211yesmaximal, characteristic, complemented
10C2×#17988468C211yesmaximal, characteristic, complemented
11C2×#17988465C211yesmaximal, characteristic
12C2×#17988465C211yesmaximal, characteristic
13C2×#17988446C211yesmaximal, characteristic, complemented
14C2×#17988444C211yesmaximal, characteristic, complemented
15C2×#95×D73C211yesmaximal, characteristic, complemented
16C2×#387×C73C211yesmaximal, characteristic, complemented
17C23×D292C2211yescharacteristic
18C23×C4×D73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C23×C4×D73C2211yescharacteristic
21C2×#14556576—28no—
22C2×#14556576C2218yes—
23C2×#14556548—28no—
24C2×#14556548C2218yescomplemented
25C22×C4⋊Dic73C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×#11924005C2211yescharacteristic
33C22×#11924005C2211yescharacteristic
34C22×#11924005C2211yescharacteristic
35C22×#11924005C2211yescharacteristic
36C22×#11924005C2211yescharacteristic
37C22×#11924005C2211yescharacteristic
38C22×#11924005C2211yescharacteristic
39C22×#11924005C2211yescharacteristic
40C22×C4×Dic73C2211yescharacteristic
41#17988528C2218yescomplemented
42#17988522C2218yescomplemented
43#17988521C2218yescomplemented
44#17988516C2218yescomplemented
45#17988479C2218yescomplemented
46#17988478C2218yescomplemented
47#17988468C2218yescomplemented
48#17988465C2218yes—
49#17988465C2218yes—
50#17988446C2218yescomplemented
51#17988444C2218yescomplemented
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60#95×D73C2218yescomplemented
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×C42×C73C2211yescharacteristic
64#387×C73C2218yescomplemented
65C2×#95×C73C2211yescharacteristic
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C2×#95×C73C2211yescharacteristic
69C24×D73C2311yescharacteristic
70C24×D73C2311yescharacteristic
71C22×D292—24no—
72C22×D292—24no—
73C22×D292—24no—
74C22×D292C2314yes—
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C22×C4×D73—24no—
82C22×C4×D73—24no—
83C22×C4×D73—24no—
84C22×C4×D73—24no—
85C22×C4×D73—24no—
86C22×C4×D73—24no—
87C22×C4×D73—42no—
88C22×C4×D73—42no—
89C22×C4×D73D418yes—
90C22×C4×D73C2314yes—
91C22×C4×D73C2314yes—
92C22×C4×D73C2314yes—
93#14556576—232no—
94#14556548—232no—
95C2×C4⋊Dic73—42no—
96C2×C4⋊Dic73C2314yes—
97C2×#11924007—24no—
98C2×#11924007—24no—
99C2×#11924007—24no—
100C2×#11924007—24no—
101C2×#11924007—42no—
102C2×#11924007C2314yes—
103C2×#11924007C2314yes—
104C2×#11924007C2314yes—
105C2×#11924007C2314yes—
106C2×#11924007C2314yes—
107C2×#11924005—24no—
108C2×#11924005—24no—
109C2×#11924005—24no—
110C2×#11924005—24no—
111C2×#11924005—24no—
112C2×#11924005—24no—
113C2×#11924005—24no—
114C2×#11924005—42no—
115C2×#11924005—42no—
116C2×#11924005C2314yes—
117C2×#11924005C2314yes—
118C2×#11924005C2314yes—
119C2×#11924005C2314yes—
120C2×#11924005C2314yes—
121C2×#11924005C2314yes—
122C2×#11924005C2314yes—
123C2×#11924005C2314yes—
124C2×#11924005C2314yes—
125C2×C4×Dic73—24no—
126C2×C4×Dic73C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129#14556498C2314yes—
130#14556498C2314yes—
131#14556498C2314yes—
132#14556498C2314yes—
133#14556498C2314yes—
134#14556498C2314yes—
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C23×C4×C73C2311yescharacteristic
139C23×C4×C73C2311yescharacteristic
140C23×C4×C73C2311yescharacteristic
141C23×C4×C73C2311yescharacteristic
142C2×C4⋊C4×C73—24no—
143C2×C4⋊C4×C73—24no—
144C2×C4⋊C4×C73C2314yes—
145C2×C4⋊C4×C73C2314yes—
146C2×C42×C73—24no—
147C2×C42×C73C2314yes—
148#95×C73C2314yes—
149#95×C73C2314yes—
150#95×C73C2314yes—
151#95×C73C2314yes—
152C23×D73—22no—
153C23×D73—22no—
154C23×D73—22no—
155C23×D73—22no—
156C23×D73—22no—
157C23×D73—22no—
158C23×D73—22no—
159C23×D73—22no—
160C23×D73—22no—
161C23×D73—22no—
162C23×D73—22no—
163C23×D73C2×D414yes—
164C23×D73#4114yes—
165C23×D73#4114yes—
166C23×D73C2412yes—
167C23×D73C2412yes—
168C2×D292—28no—
169C2×D292—28no—
170C2×D292—28no—
171C2×D292—416no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73—22no—
178C22×Dic73—22no—
179C22×Dic73—22no—
180C22×Dic73—22no—
181C22×Dic73—22no—
182C22×Dic73—22no—
183C22×Dic73—22no—
184C22×Dic73—22no—
185C22×Dic73—22no—
186C22×Dic73—22no—
187C22×Dic73—22no—
188C22×Dic73C2×D414yes—
189C22×Dic73#4114yes—
190C22×Dic73C2412yes—
191C22×Dic73C2412yes—
192C22×Dic73C2412yes—
193C22×Dic73C2412yes—
194C22×Dic73C2412yes—
195C22×Dic73C2412yes—
196C2×C4×D73—232no—
197C2×C4×D73—28no—
198C2×C4×D73—28no—
199C2×C4×D73—28no—
200C2×C4×D73—28no—
201C2×C4×D73—28no—
202C2×C4×D73—28no—
203C2×C4×D73—44no—
204C2×C4×D73—44no—
205C2×C4×D73—416no—
206C2×C4×D73—416no—
207C2×C4×D73C2×D4116yes—
208C4⋊Dic73—44no—
209#11924007—28no—
210#11924007—28no—
211#11924007—28no—
212#11924007—28no—
213#11924007—44no—
214#11924005—28no—
215#11924005—28no—
216#11924005—28no—
217#11924005—28no—
218#11924005—28no—
219#11924005—28no—
220#11924005—28no—
221#11924005—44no—
222#11924005—44no—
223C4×Dic73—28no—
224C24×C73C2411yescharacteristic
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
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×C73—22no—
241C22×C4×C73—22no—
242C22×C4×C73—22no—
243C22×C4×C73—22no—
244C22×C4×C73C2×D414yes—
245C22×C4×C73#4114yes—
246C22×C4×C73C2412yes—
247C22×C4×C73C2412yes—
248C22×C4×C73C2412yes—
249C22×C4×C73C2412yes—
250C22×C4×C73C2412yes—
251C22×C4×C73C2412yes—
252C22×C4×C73C2412yes—
253C4⋊C4×C73—28no—
254C4⋊C4×C73—28no—
255C42×C73—28no—
256C23×C73C22×D412yes—
257C23×C73C2×#4112yes—
258C23×C73C2×#4112yes—
259C23×C73C2×#4112yes—
260C23×C73C2×#4112yes—
261C23×C73H(5,𝔽2)12yes—
262C23×C732−1+412yes—
263C23×C73C2511yescharacteristic
264C22×D73—28no—
265C22×D73—28no—
266C22×D73—28no—
267C22×D73—28no—
268C22×D73—28no—
269C22×D73—28no—
270C22×D73—22no—
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—44no—
282C22×D73—44no—
283C22×D73—44no—
284C22×D73—44no—
285C22×D73—44no—
286C22×D73—44no—
287C22×D73—44no—
288C22×D73#123116yes—
289C22×D73C22×D414yes—
290C22×D73C2×#4114yes—
291C22×D73C2×#4114yes—
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—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—44no—
314C2×C4×C73—44no—
315C2×C4×C73—44no—
316C2×C4×C73—44no—
317C2×C4×C73—44no—
318C2×C4×C73C22×D414yes—
319C2×C4×C73C2×#4114yes—
320C2×Dic73—28no—
321C2×Dic73—28no—
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—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—44no—
339C2×Dic73—44no—
340C2×Dic73—44no—
341C2×Dic73—44no—
342C2×Dic73C22×D414yes—
343C2×Dic73C2×#4114yes—
344D292—416no—
345C4×D73—232no—
346C4×D73—416no—
347C4×D73—416no—
348C22×C73C2×#12314yes—
349C22×C73#53214yes—
350C22×C73#53714yes—
351C22×C73#55114yes—
352C22×C73#55114yes—
353C22×C73#55214yes—
354C22×C73#55214yes—
355C22×C73C23×D411yescharacteristic
356C22×C73C22×#4111yescharacteristic
357C22×C73C22×#4111yescharacteristic
358C22×C73C22×#4111yescharacteristic
359C22×C73C22×#4111yescharacteristic
360C22×C73C2×H(5,𝔽2)11yescharacteristic
361C22×C73C2×2−1+411yescharacteristic
362C2×D73—24no—
363C2×D73—24no—
364C2×D73—24no—
365C2×D73—24no—
366C2×D73—24no—
367C2×D73—24no—
368C2×D73—232no—
369C2×D73—42no—
370C2×D73—42no—
371C2×D73—42no—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—42no—
375C2×D73—42no—
376C2×D73—88no—
377C2×D73C2×#12318yes—
378C4×C73—24no—
379C4×C73—24no—
380C4×C73—42no—
381C4×C73—42no—
382C4×C73—42no—
383C4×C73—42no—
384C4×C73—42no—
385Dic73—24no—
386Dic73—24no—
387Dic73—42no—
388Dic73—42no—
389Dic73—42no—
390Dic73—42no—
391C2×#2498—731nomaximal, Sylow
392C2×C73#249818yescomplemented
393C2×C73C22×#12311yescharacteristic
394C2×C73C2×#53211yescharacteristic
395C2×C73C2×#53711yescharacteristic
396C2×C73C2×#55111yescharacteristic
397C2×C73C2×#55111yescharacteristic
398C2×C73C2×#55211yescharacteristic
399C2×C73C2×#55211yescharacteristic
400D73—28no—
401D73—82no—
402C22×#123—731no—
403C22×#117—731no—
404#2498—7316no—
405C2×#400—731no—
406C2×#399—731no—
407C2×#398—731no—
408C2×#397—731no—
409C2×#388—731no—
410C2×#388—731no—
411C2×#387—731no—
412C2×#387D7311yescharacteristic, complemented
413C2×#386—731no—
414C2×#386—731no—
415C2×#380—731no—
416C2×#380—731no—
417C22×#95—731no—
418C73C2×#249811yescharacteristic, complemented, Sylow
419C23×D4—731no—
420C24×C4—731no—
421C24×C4—731no—
422C24×C4—731no—
423C2×#123—738no—
424C2×#123—1468no—
425C2×#117—738no—
426C2×#117—1468no—
427C22×C4⋊C4—731no—
428C22×C4⋊C4—731no—
429C22×C4⋊C4—731no—
430C22×C4⋊C4—731no—
431C22×C4⋊C4—731no—
432C22×C4⋊C4—731no—
433C22×C4⋊C4C2×D7311yescharacteristic
434C22×C4⋊C4C2×D7311yescharacteristic
435C22×C22⋊C4—731no—
436C22×C22⋊C4—731no—
437C22×C22⋊C4—731no—
438C22×C22⋊C4—731no—
439C22×C22⋊C4—731no—
440C22×C22⋊C4—731no—
441C22×C22⋊C4—731no—
442C22×C22⋊C4—731no—
443C22×C22⋊C4—731no—
444C22×C42—731no—
445C22×C42C2×D7311yescharacteristic
446#400—738no—
447#399—738no—
448#398—738no—
449#397—738no—
450#388—738no—
451#388—738no—
452#387—738no—
453#387C2×D7318yescomplemented
454#386—738no—
455#386—738no—
456#380—738no—
457#380—738no—
458C2×#95—731no—
459C2×#95—731no—
460C2×#95—731no—
461C2×#95—731no—
462C2×#95—731no—
463C2×#95—731no—
464C2×#95—731no—
465C2×#95—731no—
466C2×#95—738no—
467C2×#95C2×D7311yescharacteristic
468C2×#95C2×D7311yescharacteristic
469C2×#95C2×D7311yescharacteristic
470C2×#95C2×D7311yescharacteristic
471C25—731no—
472C25—731no—
473C22×D4—734no—
474C22×D4—1464no—
475C22×D4—1464no—
476C22×D4—1464no—
477C23×C4—2922no—
478C23×C4—2922no—
479C23×C4—734no—
480C23×C4—734no—
481C23×C4—731no—
482C23×C4—731no—
483C23×C4—738no—
484C23×C4—734no—
485C23×C4—731no—
486C23×C4—731no—
487C23×C4—731no—
488C23×C4—731no—
489C23×C4—1464no—
490C23×C4—1464no—
491C23×C4—1464no—
492C23×C4—1464no—
493C23×C4—1464no—
494C23×C4—1464no—
495C23×C4C22×D7311yescharacteristic
496C23×C4C22×D7311yescharacteristic
497C23×C4C22×D7311yescharacteristic
498C23×C4C22×D7311yescharacteristic
499C23×C4C22×D7311yescharacteristic
500C23×C4C22×D7311yescharacteristic
501C23×C4C22×D7311yescharacteristic
502#123—14632no—
503#117—14632no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—2922no—
507C2×C4⋊C4—2922no—
508C2×C4⋊C4—734no—
509C2×C4⋊C4—734no—
510C2×C4⋊C4—734no—
511C2×C4⋊C4—734no—
512C2×C4⋊C4—734no—
513C2×C4⋊C4—734no—
514C2×C4⋊C4—1464no—
515C2×C4⋊C4—1464no—
516C2×C4⋊C4—1464no—
517C2×C4⋊C4—1464no—
518C2×C4⋊C4C22×D7314yes—
519C2×C4⋊C4C22×D7314yes—
520C2×C22⋊C4—2922no—
521C2×C22⋊C4—2922no—
522C2×C22⋊C4—734no—
523C2×C22⋊C4—734no—
524C2×C22⋊C4—734no—
525C2×C22⋊C4—734no—
526C2×C22⋊C4—734no—
527C2×C22⋊C4—734no—
528C2×C22⋊C4—734no—
529C2×C22⋊C4—734no—
530C2×C22⋊C4—734no—
531C2×C22⋊C4—1464no—
532C2×C22⋊C4—1464no—
533C2×C22⋊C4—1464no—
534C2×C22⋊C4—1464no—
535C2×C22⋊C4—1464no—
536C2×C22⋊C4—1464no—
537C2×C22⋊C4—1464no—
538C2×C42—24no—
539C2×C42—734no—
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—
550#95C22×D7314yes—
551#95C22×D7314yes—
552#95C22×D7314yes—
553#95C22×D7314yes—
554C24—734no—
555C24—734no—
556C24—734no—
557C24—732no—
558C24—732no—
559C24—1462no—
560C24—1462no—
561C24—1462no—
562C24—1462no—
563C24—1462no—
564C24—1462no—
565C24—1462no—
566C24—1462no—
567C24—1462no—
568C24—1462no—
569C24—1462no—
570C24C23×D7311yescharacteristic
571C2×D4—29216no—
572C2×D4—1468no—
573C2×D4—1468no—
574C2×D4—1468no—
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—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—29216no—
595C22×C4—2924no—
596C22×C4—2924no—
597C22×C4—29216no—
598C22×C4—734no—
599C22×C4—734no—
600C22×C4—732no—
601C22×C4—732no—
602C22×C4—7316no—
603C22×C4—732no—
604C22×C4—732no—
605C22×C4—732no—
606C22×C4—732no—
607C22×C4—1468no—
608C22×C4—1468no—
609C22×C4—1468no—
610C22×C4—1468no—
611C22×C4—1468no—
612C22×C4—14632no—
613C22×C4—1462no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1462no—
619C22×C4—1462no—
620C22×C4—1462no—
621C22×C4—1462no—
622C22×C4—1462no—
623C22×C4—1462no—
624C22×C4—1462no—
625C22×C4—1468no—
626C22×C4—1462no—
627C22×C4—1462no—
628C22×C4—1462no—
629C22×C4—1462no—
630C22×C4D4×D7314yes—
631C22×C4#1192402814yes—
632C22×C4C23×D7312yes—
633C22×C4C23×D7312yes—
634C22×C4C23×D7312yes—
635C22×C4C23×D7312yes—
636C22×C4C23×D7312yes—
637C22×C4C23×D7312yes—
638C22×C4C23×D7312yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—2924no—
642C4⋊C4—2924no—
643C4⋊C4—1468no—
644C4⋊C4—1468no—
645C4⋊C4—1468no—
646C4⋊C4—1468no—
647C22⋊C4—2924no—
648C22⋊C4—2924no—
649C22⋊C4—1468no—
650C22⋊C4—1468no—
651C22⋊C4—1468no—
652C22⋊C4—1468no—
653C22⋊C4—1468no—
654C22⋊C4—1468no—
655C22⋊C4—1468no—
656C42—28no—
657C42—1468no—
658C23—2924no—
659C23—2924no—
660C23—2924no—
661C23—2924no—
662C23—2924no—
663C23—2924no—
664C23—2924no—
665C23—734no—
666C23—734no—
667C23—734no—
668C23—7316no—
669C23—1462no—
670C23—1462no—
671C23—1462no—
672C23—1462no—
673C23—1462no—
674C23—1462no—
675C23—1462no—
676C23—1468no—
677C23—1462no—
678C23—1462no—
679C23—1462no—
680C23—1462no—
681C23—1468no—
682C23—1468no—
683C23—1468no—
684C23—1468no—
685C23—1468no—
686C23C2×D4×D7312yes—
687C23#41×D7312yes—
688C23#41×D7312yes—
689C23#41×D7312yes—
690C23C2×#1192402812yes—
691C23#1455663712yes—
692C23#1455663912yes—
693C23C24×D7311yescharacteristic
694D4—29216no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—29216no—
722C2×C4—29216no—
723C2×C4—2924no—
724C2×C4—2924no—
725C2×C4—2924no—
726C2×C4—2924no—
727C2×C4—734no—
728C2×C4—734no—
729C2×C4—14632no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1462no—
746C2×C4—1468no—
747C2×C4—1468no—
748C2×C4C2×D4×D7314yes—
749C2×C4C2×#1192402814yes—
750C22—2922no—
751C22—2922no—
752C22—2922no—
753C22—2922no—
754C22—2922no—
755C22—2922no—
756C22—2922no—
757C22—5848no—
758C22—738no—
759C22—1464no—
760C22—14632no—
761C22—1464no—
762C22—1464no—
763C22—1464no—
764C22—1464no—
765C22—1464no—
766C22#123×D7314yes—
767C22#1798913414yes—
768C22#1798916714yes—
769C22#1798926114yes—
770C22#1798926214yes—
771C22#1798926914yes—
772C22#1798927814yes—
773C22C22×D4×D7311yescharacteristic
774C22C2×#41×D7311yescharacteristic
775C22C2×#41×D7311yescharacteristic
776C22C2×#41×D7311yescharacteristic
777C22C22×#1192402811yescharacteristic
778C22C2×#1455663711yescharacteristic
779C22C2×#1455663911yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—2922no—
788C4—2922no—
789C4—2922no—
790C4—2922no—
791C4—1464no—
792C4—1464no—
793C2—5842no—
794C2—1468no—
795C2#2261437218yesdirect product factor
796C2C2×#123×D7311yescharacteristic
797C2C2×#1798913411yescharacteristic
798C2C2×#1798916711yescharacteristic
799C2C2×#1798926111yescharacteristic
800C2C2×#1798926211yescharacteristic
801C2C2×#1798926911yescharacteristic
802C2C2×#1798927811yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#387×C73C2
socleC24×C73C24
prime radicalC23×D292C22
hypercenterC2×#387D73
hypocenterC73C2×#2498
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×#14556548C2semidirect
3. #22614372C2direct (N × H)
4. C2×#17988528C2semidirect
5. C2×#17988522C2semidirect
6. C2×#17988521C2semidirect
7. C2×#17988516C2semidirect
8. C2×#17988479C2semidirect
9. C2×#17988478C2semidirect
10. C2×#17988468C2semidirect
13. C2×#17988446C2semidirect
14. C2×#17988444C2semidirect
15. C2×#95×D73C2semidirect
16. C2×#387×C73C2semidirect
24. C2×#14556548C22semidirect
41. #17988528C22semidirect
42. #17988522C22semidirect
43. #17988521C22semidirect
44. #17988516C22semidirect
45. #17988479C22semidirect
46. #17988478C22semidirect
47. #17988468C22semidirect
50. #17988446C22semidirect
51. #17988444C22semidirect
60. #95×D73C22semidirect
64. #387×C73C22semidirect
392. C2×C73#2498semidirect
412. C2×#387D73semidirect
418. C73C2×#2498semidirect
453. #387C2×D73semidirect
795. C2#22614372direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565762
C22×#145565482
#226143722
C2×#179885282
C2×#179885222
C2×#179885212
C2×#179885162
C2×#179884792
C2×#179884782
C2×#179884682
C2×#179884652
C2×#179884462
C2×#179884442
C2×#95×D732
C2×#387×C732
C2×#249873