Finite Group Databasebeta

← #33009072

Subgroups — #33009072

Order 18688.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988444C211yesmaximal, characteristic
2C2×#17988444C211yesmaximal, characteristic
3C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
4C2×C4×#11924005C211yesmaximal, characteristic
5#22608192C212yesmaximal, complemented
6#22608173C212yesmaximal
7#22608167C212yesmaximal
8#22608163C212yesmaximal, complemented
9#22608161C211yesmaximal, characteristic, complemented
10#22608160C211yesmaximal, characteristic, complemented
11C2×#389×C73C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2211yescharacteristic
15C22×#11924005C2211yescharacteristic
16C22×#11924005C2212yes—
17C22×#11924005C2211yescharacteristic
18C22×#11924005C2212yes—
19C22×C4×Dic73C2211yescharacteristic
20C22×C4×Dic73C2212yes—
21#17988444—24no—
22#17988444C418yescomplemented
23C4⋊C4×Dic73—24no—
24C4×#11924005—24no—
25C2×#14556498C2212yes—
26C2×#14556498C2211yescharacteristic
27C2×#14556498C2212yes—
28C2×#14556498C2211yescharacteristic
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C22×C4⋊C4×C73C2212yes—
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C42×C73C2211yescharacteristic
38#389×C73—24no—
39C2×#95×C73C2212yes—
40C24×D73C2311yescharacteristic
41C23×Dic73C2312yes—
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2312yes—
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C22×C4×D73—22no—
47C22×C4×D73—22no—
48C22×C4×D73—22no—
49C22×C4×D73—22no—
50C22×C4×D73—22no—
51C22×C4×D73—22no—
52C22×C4×D73C2×C414yes—
53C2×C4⋊Dic73—22no—
54C2×C4⋊Dic73—22no—
55C2×C4⋊Dic73—22no—
56C2×C4⋊Dic73—22no—
57C2×C4⋊Dic73—22no—
58C2×C4⋊Dic73C2×C414yes—
59C2×#11924005—22no—
60C2×#11924005—22no—
61C2×#11924005—22no—
62C2×#11924005—22no—
63C2×#11924005—24no—
64C2×#11924005—24no—
65C2×#11924005—22no—
66C2×#11924005—42no—
67C2×#11924005—42no—
68C2×#11924005—42no—
69C2×#11924005C2×C418yes—
70C2×#11924005Q814yes—
71C2×C4×Dic73—24no—
72C2×C4×Dic73—22no—
73C2×C4×Dic73—22no—
74C2×C4×Dic73—42no—
75C2×C4×Dic73—42no—
76C2×C4×Dic73D414yes—
77#14556498—22no—
78#14556498—22no—
79#14556498—24no—
80#14556498—24no—
81#14556498—24no—
82#14556498—42no—
83#14556498—42no—
84#14556498—42no—
85#14556498C2×C418yes—
86C23×C4×C73C2312yes—
87C23×C4×C73C2312yes—
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—24no—
96C2×C4⋊C4×C73—24no—
97C2×C4⋊C4×C73—42no—
98C2×C4⋊C4×C73C2×C414yes—
99C2×C4⋊C4×C73D414yes—
100C2×C42×C73—22no—
101C2×C42×C73—22no—
102C2×C42×C73—22no—
103#95×C73—24no—
104C23×D73—21no—
105C23×D73—21no—
106C23×D73—21no—
107C23×D73—21no—
108C23×D73—21no—
109C23×D73—21no—
110C23×D73—21no—
111C23×D73—21no—
112C23×D73—21no—
113C23×D73—21no—
114C23×D73—21no—
115C23×D73—21no—
116C23×D73C22×C412yes—
117C23×D73C2×Q812yes—
118C23×D73#4112yes—
119C22×Dic73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—22no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—22no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—21no—
141C22×Dic73—22no—
142C22×Dic73—22no—
143C22×Dic73—22no—
144C22×Dic73—22no—
145C22×Dic73—22no—
146C22×Dic73—22no—
147C22×Dic73—22no—
148C22×Dic73C22×C412yes—
149C22×Dic73C22×C414yes—
150C22×Dic73C2×D412yes—
151C22×Dic73C2×D412yes—
152C22×Dic73C2×Q812yes—
153C22×Dic73#4112yes—
154C2×C4×D73—28no—
155C2×C4×D73—28no—
156C2×C4×D73—28no—
157C2×C4×D73—44no—
158C2×C4×D73—44no—
159C2×C4×D73—44no—
160C2×C4×D73—44no—
161C4⋊Dic73—28no—
162C4⋊Dic73—44no—
163#11924005—28no—
164#11924005—28no—
165#11924005—48no—
166#11924005—48no—
167C4×Dic73—28no—
168C4×Dic73—48no—
169C24×C73C2411yescharacteristic
170C22×C4×C73—21no—
171C22×C4×C73—22no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—22no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—22no—
186C22×C4×C73—21no—
187C22×C4×C73—22no—
188C22×C4×C73—22no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—22no—
192C22×C4×C73—22no—
193C22×C4×C73—21no—
194C22×C4×C73C22×C414yes—
195C22×C4×C73C22×C412yes—
196C22×C4×C73C2×D412yes—
197C22×C4×C73C2×D414yes—
198C22×C4×C73C2×D412yes—
199C22×C4×C73C2×Q812yes—
200C22×C4×C73#4112yes—
201C22×C4×C73#4112yes—
202C22×C4×C73#4112yes—
203C22×C4×C73#4112yes—
204C22×C4×C73#4112yes—
205C4⋊C4×C73—28no—
206C4⋊C4×C73—28no—
207C4⋊C4×C73—48no—
208C42×C73—44no—
209C23×C73C23×C411yescharacteristic
210C23×C73C22×D411yescharacteristic
211C23×C73C22×D411yescharacteristic
212C23×C73C22×Q811yescharacteristic
213C23×C73C2×#4111yescharacteristic
214C23×C73C2×#4111yescharacteristic
215C23×C73C2×#4111yescharacteristic
216C23×C73C2×#4111yescharacteristic
217C23×C73C2×#4111yescharacteristic
218C23×C73C2×#4111yescharacteristic
219C23×C73C2×#4111yescharacteristic
220C23×C73H(5,𝔽2)11yescharacteristic
221C23×C73H(5,𝔽2)11yescharacteristic
222C23×C73H(5,𝔽2)11yescharacteristic
223C23×C732−1+411yescharacteristic
224C22×D73—22no—
225C22×D73—22no—
226C22×D73—22no—
227C22×D73—22no—
228C22×D73—22no—
229C22×D73—22no—
230C22×D73—22no—
231C22×D73—22no—
232C22×D73—22no—
233C22×D73—22no—
234C22×D73—22no—
235C22×D73—22no—
236C22×D73—22no—
237C22×D73—22no—
238C22×D73—22no—
239C22×D73—22no—
240C22×D73—22no—
241C22×D73—22no—
242C22×D73—41no—
243C22×D73—41no—
244C22×D73—41no—
245C22×D73—41no—
246C22×D73—41no—
247C22×D73—41no—
248C22×D73—41no—
249C22×D73—41no—
250C22×D73—41no—
251C22×D73—41no—
252C22×D73—41no—
253C22×D73—41no—
254C22×D73—41no—
255C22×D73—41no—
256C22×D73—41no—
257C22×D73—41no—
258C22×D73C4×Q814yes—
259C2×C4×C73—24no—
260C2×C4×C73—24no—
261C2×C4×C73—24no—
262C2×C4×C73—24no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—24no—
267C2×C4×C73—24no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—42no—
274C2×C4×C73—41no—
275C2×C4×C73—42no—
276C2×C4×C73—41no—
277C2×C4×C73—42no—
278C2×C4×C73—41no—
279C2×C4×C73—42no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—42no—
283C2×C4×C73—42no—
284C2×C4×C73—42no—
285C2×C4×C73—42no—
286C2×C4×C73—41no—
287C2×C4×C73#11714yes—
288C2×C4×C73C4×D414yes—
289C2×C4×C73C4×D414yes—
290C2×C4×C73#12114yes—
291C2×C4×C73#12314yes—
292C2×C4×C73#12414yes—
293C2×C4×C73#12614yes—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—24no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—24no—
305C2×Dic73—24no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73C22⋊Q814yes—
329C4×D73—416no—
330C22×C73C2×#11711yescharacteristic
331C22×C73C2×C4×D411yescharacteristic
332C22×C73C2×C4×D411yescharacteristic
333C22×C73C2×C4×Q811yescharacteristic
334C22×C73C4×#4111yescharacteristic
335C22×C73#51811yescharacteristic
336C22×C73#52011yescharacteristic
337C22×C73C2×#12111yescharacteristic
338C22×C73C2×C22⋊Q811yescharacteristic
339C22×C73C2×#12311yescharacteristic
340C22×C73#52511yescharacteristic
341C22×C73C2×#12411yescharacteristic
342C22×C73C2×#12611yescharacteristic
343C22×C73#52911yescharacteristic
344C22×C73#53311yescharacteristic
345C22×C73#53511yescharacteristic
346C22×C73#53711yescharacteristic
347C22×C73#54011yescharacteristic
348C22×C73#54211yescharacteristic
349C22×C73#54611yescharacteristic
350C22×C73#54611yescharacteristic
351C22×C73D4×Q811yescharacteristic
352C22×C73#55011yescharacteristic
353C22×C73#55211yescharacteristic
354C22×C73#55311yescharacteristic
355C22×C73#55311yescharacteristic
356C22×C73#55311yescharacteristic
357C22×C73#55311yescharacteristic
358C22×C73#55311yescharacteristic
359C22×C73#55411yescharacteristic
360C22×C73#55411yescharacteristic
361C22×C73#55411yescharacteristic
362C22×C73#55511yescharacteristic
363C22×C73#55611yescharacteristic
364C22×C73#55611yescharacteristic
365C2×D73—24no—
366C2×D73—24no—
367C2×D73—24no—
368C2×D73—42no—
369C2×D73—42no—
370C2×D73—42no—
371C2×D73—42no—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—42no—
375C2×D73—42no—
376C2×D73—42no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C4×C73—44no—
381C4×C73—44no—
382C4×C73—42no—
383C4×C73—42no—
384C4×C73#38818yes—
385Dic73—24no—
386Dic73—44no—
387Dic73—42no—
388Dic73—42no—
389Dic73—82no—
390#13993—731nomaximal, Sylow
391C2×C73C2×#38811yescharacteristic
392C2×C73C4×C22⋊Q811yescharacteristic
393C2×C73#232411yescharacteristic
394C2×C73#234511yescharacteristic
395C2×C73#234711yescharacteristic
396C2×C73#236011yescharacteristic
397C2×C73#236311yescharacteristic
398C2×C73#248511yescharacteristic
399C2×C73#248711yescharacteristic
400C2×C73#249011yescharacteristic
401C2×C73#249211yescharacteristic
402C2×C73#249411yescharacteristic
403C2×C73#249711yescharacteristic
404C2×C73#253511yescharacteristic
405C2×C73#253811yescharacteristic
406D73—44no—
407C2×#389D7311yescharacteristic, complemented
408C2×#380—731no—
409C2×#380—731no—
410C2×C4×C4⋊C4—731no—
411C2×C4×C22⋊C4—731no—
412#1443—732no—
413#1439—732no—
414#1437—732no—
415#1436—732no—
416C4⋊#95—731no—
417C4⋊#95—731no—
418C73#1399311yescharacteristic, complemented, Sylow
419C24×C4—731no—
420C22×C4⋊C4—731no—
421C22×C4⋊C4—731no—
422C22×C4⋊C4C2×D7312yes—
423C22×C4⋊C4C2×D7311yescharacteristic
424C22×C4⋊C4C2×D7311yescharacteristic
425C22×C22⋊C4—732no—
426C22×C22⋊C4—732no—
427C22×C22⋊C4—731no—
428C22×C22⋊C4—731no—
429C22×C42—732no—
430C22×C42—731no—
431C22×C42C2×D7311yescharacteristic
432#389—24no—
433#380—738no—
434#380—1464no—
435C4×C4⋊C4—1464no—
436C4×C22⋊C4—1464no—
437C2×#95—732no—
438C2×#95—732no—
439C2×#95—732no—
440C2×#95—732no—
441C2×#95—732no—
442C2×#95—731no—
443C2×#95—732no—
444C2×#95—732no—
445C2×#95—731no—
446C2×#95C2×D7312yes—
447C25—731no—
448C23×C4—731no—
449C23×C4—732no—
450C23×C4—731no—
451C23×C4—731no—
452C23×C4—734no—
453C23×C4—732no—
454C23×C4—1462no—
455C23×C4—1462no—
456C23×C4—1462no—
457C23×C4—1462no—
458C23×C4—1462no—
459C23×C4—1462no—
460C23×C4C22×D7312yes—
461C23×C4C22×D7312yes—
462C23×C4C22×D7311yescharacteristic
463C23×C4C22×D7311yescharacteristic
464C23×C4C22×D7311yescharacteristic
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—734no—
473C2×C4⋊C4—1462no—
474C2×C4⋊C4—1462no—
475C2×C4⋊C4—1462no—
476C2×C4⋊C4—1462no—
477C2×C4⋊C4—1462no—
478C2×C4⋊C4C4×D7314yes—
479C2×C4⋊C4C22⋊D7314yes—
480C2×C22⋊C4—2922no—
481C2×C22⋊C4—2922no—
482C2×C22⋊C4—2922no—
483C2×C22⋊C4—738no—
484C2×C22⋊C4—734no—
485C2×C22⋊C4—1464no—
486C2×C22⋊C4—1464no—
487C2×C22⋊C4—1462no—
488C2×C22⋊C4—1462no—
489C2×C22⋊C4—1462no—
490C2×C22⋊C4—1462no—
491C2×C22⋊C4—1462no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—2922no—
496C2×C42—2922no—
497C2×C42—734no—
498C2×C42—1464no—
499C2×C42—1462no—
500C2×C42—1462no—
501#95—24no—
502#95—2922no—
503#95—2922no—
504#95—2922no—
505#95—738no—
506#95—1464no—
507#95—1462no—
508#95—1462no—
509#95—1464no—
510#95—1464no—
511C24—732no—
512C24—732no—
513C24—732no—
514C24—1461no—
515C24—1461no—
516C24—1461no—
517C24—1461no—
518C24—1461no—
519C24—1461no—
520C24—1461no—
521C24—1461no—
522C24—1461no—
523C24—1461no—
524C24—1461no—
525C24—1461no—
526C24C23×D7311yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—2924no—
552C22×C4—2924no—
553C22×C4—2924no—
554C22×C4—2924no—
555C22×C4—732no—
556C22×C4—732no—
557C22×C4—732no—
558C22×C4—732no—
559C22×C4—734no—
560C22×C4—732no—
561C22×C4—1462no—
562C22×C4—1462no—
563C22×C4—1462no—
564C22×C4—1462no—
565C22×C4—1462no—
566C22×C4—1462no—
567C22×C4—1462no—
568C22×C4—1461no—
569C22×C4—1462no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1462no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4—1462no—
581C22×C4—1461no—
582C22×C4—1462no—
583C22×C4—1462no—
584C22×C4—1462no—
585C22×C4—1461no—
586C22×C4—1468no—
587C22×C4—1468no—
588C22×C4—1468no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4C2×C4×D7314yes—
594C22×C4C2×C4×D7312yes—
595C22×C4D4×D7312yes—
596C22×C4C2×C22⋊D7314yes—
597C22×C4C2×C22⋊D7312yes—
598C22×C4Q8×D7312yes—
599C22×C4#1192402712yes—
600C22×C4#1192402712yes—
601C22×C4#1192402812yes—
602C22×C4#1192402912yes—
603C22×C4#1192402912yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—48no—
607C4⋊C4—2924no—
608C4⋊C4—1468no—
609C22⋊C4—2928no—
610C22⋊C4—2928no—
611C22⋊C4—1468no—
612C22⋊C4—1468no—
613C42—44no—
614C42—2928no—
615C42—1468no—
616C23—2921no—
617C23—2921no—
618C23—2921no—
619C23—2921no—
620C23—2921no—
621C23—2921no—
622C23—2921no—
623C23—2921no—
624C23—2921no—
625C23—2921no—
626C23—2921no—
627C23—2921no—
628C23—2921no—
629C23—2921no—
630C23—2921no—
631C23—2921no—
632C23—734no—
633C23—1462no—
634C23—1462no—
635C23—1462no—
636C23—1462no—
637C23—1462no—
638C23—1462no—
639C23—1462no—
640C23—1462no—
641C23—1462no—
642C23—1462no—
643C23—1462no—
644C23—1462no—
645C23—1462no—
646C23—1462no—
647C23—1462no—
648C23—1462no—
649C23—1462no—
650C23—1462no—
651C23C22×C4×D7311yescharacteristic
652C23C2×D4×D7311yescharacteristic
653C23C22×C22⋊D7311yescharacteristic
654C23C2×Q8×D7311yescharacteristic
655C23#41×D7311yescharacteristic
656C23#41×D7311yescharacteristic
657C23C2×#1192402711yescharacteristic
658C23C2×#1192402711yescharacteristic
659C23C2×#1192402811yescharacteristic
660C23C2×#1192402911yescharacteristic
661C23C2×#1192402911yescharacteristic
662C23#1455663611yescharacteristic
663C23#1455663711yescharacteristic
664C23#1455663711yescharacteristic
665C23#1455663911yescharacteristic
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—2922no—
695C2×C4—2922no—
696C2×C4—2922no—
697C2×C4—2922no—
698C2×C4—2921no—
699C2×C4—2921no—
700C2×C4—2921no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—29216no—
707C2×C4—2922no—
708C2×C4—2922no—
709C2×C4—2922no—
710C2×C4—2922no—
711C2×C4—2922no—
712C2×C4—2922no—
713C2×C4—2922no—
714C2×C4—734no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1464no—
719C2×C4—1462no—
720C2×C4—1464no—
721C2×C4—1464no—
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#1455654914yes—
731C2×C4C4×C22⋊D7314yes—
732C2×C4#1455655314yes—
733C2×C4#1455656314yes—
734C2×C4#1455657614yes—
735C2×C4#1455658014yes—
736C2×C4#1455658614yes—
737C22—2922no—
738C22—2922no—
739C22—2922no—
740C22—2922no—
741C22—2922no—
742C22—2922no—
743C22—2922no—
744C22—2922no—
745C22—2922no—
746C22—2922no—
747C22—2922no—
748C22—2922no—
749C22—1464no—
750C22—1464no—
751C22—1464no—
752C22C2×#1455654911yescharacteristic
753C22C2×C4×C22⋊D7311yescharacteristic
754C22C2×#1455655311yescharacteristic
755C22C4×Q8×D7311yescharacteristic
756C22C4×#1192402711yescharacteristic
757C22#1798905911yescharacteristic
758C22#1798906911yescharacteristic
759C22C2×#1455656311yescharacteristic
760C22C22⋊Q8×D7311yescharacteristic
761C22C2×#1455657611yescharacteristic
762C22#1798909711yescharacteristic
763C22C2×#1455658011yescharacteristic
764C22C2×#1455658611yescharacteristic
765C22#1798912211yescharacteristic
766C22#1798914211yescharacteristic
767C22#1798915311yescharacteristic
768C22#1798916711yescharacteristic
769C22#1798919311yescharacteristic
770C22#1798921111yescharacteristic
771C22#1798922511yescharacteristic
772C22#1798923111yescharacteristic
773C22Q8×C22⋊D7311yescharacteristic
774C22#1798925611yescharacteristic
775C22#1798927811yescharacteristic
776C22#1798928411yescharacteristic
777C22#1798928711yescharacteristic
778C22#1798928911yescharacteristic
779C22#1798929011yescharacteristic
780C22#1798929011yescharacteristic
781C22#1798929511yescharacteristic
782C22#1798929711yescharacteristic
783C22#1798929811yescharacteristic
784C22#1798930211yescharacteristic
785C22#1798930811yescharacteristic
786C22#1798931111yescharacteristic
787C4—44no—
788C4—42no—
789C4—42no—
790C4—44no—
791C4—2922no—
792C4—2924no—
793C4—2922no—
794C4—5842no—
795C4—1464no—
796C4#1798847718yes—
797C2—2924no—
798C2C2×#1798847711yescharacteristic
799C2#2261246111yescharacteristic
800C2#2261262211yescharacteristic
801C2#2261280711yescharacteristic
802C2#2261282311yescharacteristic
803C2#2261293211yescharacteristic
804C2#2261296511yescharacteristic
805C2#2261422611yescharacteristic
806C2#2261424611yescharacteristic
807C2#2261428611yescharacteristic
808C2#2261430811yescharacteristic
809C2#2261432911yescharacteristic
810C2#2261436211yescharacteristic
811C2#2261483011yescharacteristic
812C2#2261485011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#389×C73C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenterC2×#389D73
hypocenterC73#13993
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic73C2semidirect
5. #22608192C2semidirect
8. #22608163C2semidirect
9. #22608161C2semidirect
10. #22608160C2semidirect
11. C2×#389×C73C2semidirect
22. #17988444C4semidirect
407. C2×#389D73semidirect
418. C73#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#179884442
C2×C4⋊C4×Dic732
C2×C4×#119240052
#226081922
#226081732
#226081672
#226081632
#226081612
#226081602
C2×#389×C732
#1399373