Finite Group Databasebeta

← #33095627

Subgroups — #33095627

Order 18688.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989115C211yesmaximal, characteristic
2C2×#17988648C211yesmaximal, characteristic, complemented
3#22610870C211yesmaximal, characteristic, complemented
4#22610866C211yesmaximal, characteristic, complemented
5#22610728C211yesmaximal, characteristic, complemented
6#22610724C211yesmaximal, characteristic, complemented
7#22610228C211yesmaximal, characteristic, complemented
8#22610228C211yesmaximal, characteristic, complemented
9#22610223C211yesmaximal, characteristic, complemented
10#22610223C211yesmaximal, characteristic, complemented
11#22609912C211yesmaximal, characteristic, complemented
12#22609912C211yesmaximal, characteristic, complemented
13#22609908C211yesmaximal, characteristic, complemented
14#22609908C211yesmaximal, characteristic, complemented
15C2×#424×C73C211yesmaximal, characteristic, complemented
16#17989115—24no—
17#17989115—24no—
18C2×#14556586C411yescharacteristic
19C2×#14556584C411yescharacteristic
20C2×#14556581C411yescharacteristic
21C2×#14556577C411yescharacteristic
22C2×#14556576C411yescharacteristic
23C2×#14556573C411yescharacteristic
24C2×#14556569C411yescharacteristic
25C2×#14556564C411yescharacteristic
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×D292C2211yescharacteristic
28C2×C4×C22⋊D73C2211yescharacteristic
29C2×C4×C22⋊D73C2211yescharacteristic
30C2×#14556548C2211yescharacteristic
31C2×C42×D73C2211yescharacteristic
32#17988648—24no—
33C2×C4⋊#10596831C2211yescharacteristic
34C2×C4⋊#10596831C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×C22⋊#10596831C2211yescharacteristic
37C2×#14556503C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×#14556503C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42C2×#14556503C2211yescharacteristic
43C2×#14556503C2211yescharacteristic
44C2×#14556503C2211yescharacteristic
45C2×#14556502C2211yescharacteristic
46C2×C4×#10596831C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56C23×C8×C73C2211yescharacteristic
57C2×#117×C73C2211yescharacteristic
58#424×C73—24no—
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×C4⋊C8×C73C2211yescharacteristic
61C2×C4⋊C8×C73C2211yescharacteristic
62C2×C4⋊C8×C73C2211yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×D292C2×C411yescharacteristic
65C22×C22⋊D73C2×C411yescharacteristic
66C22×C22⋊D73C2×C411yescharacteristic
67C22×C4×D73C2×C411yescharacteristic
68C22×C4×D73C2×C411yescharacteristic
69C22×C4×D73C2311yescharacteristic
70C22×C4×D73C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556586—24no—
76#14556584—24no—
77#14556581—24no—
78#14556577—24no—
79#14556576—24no—
80#14556573—24no—
81#14556569—24no—
82#14556564—24no—
83C4×Dic146—22no—
84C4×Dic146—22no—
85C4×D292—22no—
86C4×D292—22no—
87C4×C22⋊D73—22no—
88C4×C22⋊D73—22no—
89C4×C22⋊D73—22no—
90C4×C22⋊D73—22no—
91#14556548—22no—
92#14556548—22no—
93C2×C4⋊Dic73C2×C411yescharacteristic
94C2×C4⋊Dic73C2×C411yescharacteristic
95C2×#11924007C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924007C2×C411yescharacteristic
101C2×C22⋊Dic73C2×C411yescharacteristic
102C2×C22⋊Dic73C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×#11924005C2×C411yescharacteristic
106C2×#11924005C2×C411yescharacteristic
107C2×#11924005C2×C411yescharacteristic
108C2×#11924005C2×C411yescharacteristic
109C2×C4×Dic73C2×C411yescharacteristic
110C2×C4×Dic73C2×C411yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C42×D73—22no—
114C42×D73—22no—
115C4⋊#10596831—22no—
116C4⋊#10596831—22no—
117C22⋊#10596831—22no—
118C22⋊#10596831—22no—
119#14556503—41no—
120#14556503—41no—
121#14556503—41no—
122#14556503—41no—
123#14556503—41no—
124#14556503—41no—
125#14556503—41no—
126#14556503—41no—
127#14556502—22no—
128C4×#10596831—22no—
129C23×C4×C73C2311yescharacteristic
130C2×M16×C73—22no—
131C2×M16×C73—41no—
132C2×M16×C73—41no—
133C22×C8×C73—22no—
134C22×C8×C73—41no—
135C22×C8×C73—41no—
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139C22×C8×C73C2311yescharacteristic
140#117×C73D414yes—
141#117×C73D414yes—
142C2×C4⋊C4×C73C2×C411yescharacteristic
143C2×C4⋊C4×C73C2×C411yescharacteristic
144C2×C22⋊C4×C73C2×C411yescharacteristic
145C2×C22⋊C4×C73C2×C411yescharacteristic
146C2×C42×C73C2311yescharacteristic
147C2×C42×C73C2311yescharacteristic
148C4⋊C8×C73—22no—
149C4⋊C8×C73—22no—
150C4⋊C8×C73—22no—
151C4⋊C8×C73—22no—
152C23×D73C22×C411yescharacteristic
153C23×D73C22×C411yescharacteristic
154C2×Dic146—22no—
155C2×Dic146—22no—
156C2×Dic146—41no—
157C2×D292—22no—
158C2×D292—22no—
159C2×D292—41no—
160C2×C22⋊D73—22no—
161C2×C22⋊D73—22no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73—22no—
164C2×C22⋊D73—41no—
165C2×C22⋊D73—41no—
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C2×C4×D73—22no—
173C2×C4×D73—22no—
174C2×C4×D73—22no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73—21no—
183C2×C4×D73—21no—
184C2×C4×D73—21no—
185C2×C4×D73—21no—
186C2×C4×D73—21no—
187C2×C4×D73—22no—
188C2×C4×D73—41no—
189C2×C4×D73—41no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831—21no—
199C2×#10596831—21no—
200C2×#10596831—21no—
201C2×#10596831—21no—
202C4⋊Dic73—22no—
203C4⋊Dic73—22no—
204#11924007—22no—
205#11924007—22no—
206#11924007—22no—
207#11924007—22no—
208#11924007—22no—
209#11924007—22no—
210C22⋊Dic73—22no—
211C22⋊Dic73—22no—
212#11924005—22no—
213#11924005—22no—
214#11924005—22no—
215#11924005—22no—
216#11924005—22no—
217#11924005—22no—
218C4×Dic73—22no—
219C4×Dic73—22no—
220C4×Dic73—21no—
221C4×Dic73—21no—
222C4×Dic73—21no—
223C4×Dic73—21no—
224C24×C73C22×C411yescharacteristic
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73C22×C411yescharacteristic
230C22×C4×C73C22×C411yescharacteristic
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C2×D412yes—
235C22×C4×C73C2×D412yes—
236C22×C4×C73C2411yescharacteristic
237M16×C73—44no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—44no—
251C4⋊C4×C73C22⋊C414yes—
252C4⋊C4×C73C22⋊C414yes—
253C22⋊C4×C73C22⋊C414yes—
254C22⋊C4×C73C22⋊C414yes—
255C42×C73C2×D412yes—
256C42×C73C2×D412yes—
257C42×C73C2×D412yes—
258C42×C73C2×D412yes—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73C2×C22⋊C412yes—
266C23×C73C23×C411yescharacteristic
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—21no—
280C22×D73#13112yes—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73C2×C22⋊C412yes—
296C2×C4×C73C2×C22⋊C412yes—
297C2×C4×C73C2×C22⋊C412yes—
298C2×C4×C73C2×C22⋊C412yes—
299C2×C4×C73C2×C22⋊C412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C22×D411yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C2×C4×C732−1+411yescharacteristic
305C2×C4×C732−1+411yescharacteristic
306C22⋊D73—44no—
307C22⋊D73—44no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—21no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73#13112yes—
326D292—44no—
327C4×D73—44no—
328C4×D73—44no—
329C4×D73—41no—
330C4×D73—41no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335C4×D73—41no—
336C4×D73—41no—
337Dic146—44no—
338C8×C73—41no—
339C8×C73—41no—
340C8×C73—41no—
341C8×C73—41no—
342#10596831—41no—
343#10596831—41no—
344#10596831—41no—
345#10596831—41no—
346C22×C73—22no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73C22×C22⋊C411yescharacteristic
354C22×C73#52011yescharacteristic
355C22×C73#52011yescharacteristic
356C22×C73C2×#13111yescharacteristic
357C22×C73C2×#13111yescharacteristic
358C22×C73#56811yescharacteristic
359C22×C73#56811yescharacteristic
360C2×D73—22no—
361C2×D73—22no—
362C2×D73—22no—
363C2×D73—41no—
364C2×D73—41no—
365C2×D73—41no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—22no—
377C4×C73—22no—
378C4×C73—22no—
379C4×C73#53511yescharacteristic
380C4×C73#53611yescharacteristic
381C4×C73#53711yescharacteristic
382C4×C73#53711yescharacteristic
383Dic73—22no—
384Dic73—41no—
385Dic73—41no—
386Dic73—41no—
387Dic73—41no—
388Dic73—41no—
389#21855—731nomaximal, Sylow
390C2×C73—42no—
391C2×C73#231111yescharacteristic
392C2×C73#288011yescharacteristic
393C2×C73#288011yescharacteristic
394C2×C73#299211yescharacteristic
395C2×C73#299311yescharacteristic
396C2×C73#299411yescharacteristic
397C2×C73#299511yescharacteristic
398D73—42no—
399D73—81no—
400C2×#529—731no—
401C2×#433—731no—
402C2×#424D7311yescharacteristic, complemented
403#1985—731no—
404#1984—731no—
405#1955—731no—
406#1954—731no—
407#1870—731no—
408#1870—731no—
409#1869—731no—
410#1869—731no—
411#1798—731no—
412#1798—731no—
413#1797—731no—
414#1797—731no—
415C73#2185511yescharacteristic, complemented, Sylow
416C22×M16C2×D7311yescharacteristic
417C23×C8C2×D7311yescharacteristic
418#529—1464no—
419#529—1464no—
420C2×#126—731no—
421C2×#126—731no—
422C2×#125—731no—
423C2×#124—731no—
424C2×#123—731no—
425C2×#123—731no—
426C2×C22⋊Q8—731no—
427C2×#121—731no—
428C2×C4×Q8—731no—
429C2×C4×D4—731no—
430C2×C4×D4—731no—
431C2×C4×D4—731no—
432C2×#117—731no—
433C2×#117C2×D7311yescharacteristic
434C22×C42—731no—
435#433—1464no—
436#424—24no—
437C2×C4⋊C8—731no—
438C2×C4⋊C8—731no—
439C2×C4⋊C8C2×D7311yescharacteristic
440C2×C4⋊C8C2×D7311yescharacteristic
441C2×C4⋊C8C2×D7311yescharacteristic
442C2×C4⋊C8C2×D7311yescharacteristic
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×C22⋊C8—731no—
451C2×C22⋊C8—731no—
452C2×C22⋊C8—731no—
453C2×#97—731no—
454C2×C4×C8—731no—
455#336—731no—
456#336—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336—731no—
462#336—731no—
463C22×Q8—731no—
464C22×D4—731no—
465C22×D4—731no—
466C22×D4—731no—
467C23×C4—731no—
468C23×C4—731no—
469C23×C4—731no—
470C23×C4—731no—
471C23×C4C22×D7311yescharacteristic
472C2×M16—22no—
473C2×M16—41no—
474C2×M16—41no—
475C22×C8—22no—
476C22×C8—41no—
477C22×C8—41no—
478C22×C8—731no—
479C22×C8—731no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8C22×D7311yescharacteristic
483C22×C8C22×D7311yescharacteristic
484C22×C8C22×D7311yescharacteristic
485C22×C8C22×D7311yescharacteristic
486#126—1464no—
487#126—1464no—
488#125—1464no—
489#124—1464no—
490#123—1464no—
491#123—1464no—
492C22⋊Q8—1464no—
493#121—1464no—
494C4×Q8—1462no—
495C4×Q8—1462no—
496C4×D4—1462no—
497C4×D4—1462no—
498C4×D4—1462no—
499C4×D4—1462no—
500C4×D4—1462no—
501C4×D4—1462no—
502#117—1462no—
503#117—1462no—
504#117D29214yes—
505#117C22⋊D7314yes—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4C4×D7311yescharacteristic
515C2×C4⋊C4C4×D7311yescharacteristic
516C2×C22⋊C4—731no—
517C2×C22⋊C4—731no—
518C2×C22⋊C4—731no—
519C2×C22⋊C4—731no—
520C2×C22⋊C4—731no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4C4×D7311yescharacteristic
525C2×C22⋊C4C4×D7311yescharacteristic
526C2×C42—731no—
527C2×C42—731no—
528C2×C42—731no—
529C2×C42—731no—
530C2×C42—1462no—
531C2×C42—1462no—
532C2×C42C22×D7311yescharacteristic
533C2×C42C22×D7311yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—22no—
537C4⋊C8—22no—
538C4⋊C8—1462no—
539C4⋊C8—1462no—
540C22⋊C8—2921no—
541C22⋊C8—2921no—
542C22⋊C8—2921no—
543C22⋊C8—2921no—
544C22⋊C8—2921no—
545C22⋊C8—2921no—
546C22⋊C8—2921no—
547C22⋊C8—2921no—
548C22⋊C8—1462no—
549C22⋊C8—1462no—
550#97—1462no—
551C4×C8—1462no—
552C24—731no—
553C24—731no—
554C24C2×C4×D7311yescharacteristic
555C2×Q8—2921no—
556C2×Q8—1462no—
557C2×Q8—1462no—
558C2×D4—2921no—
559C2×D4—2921no—
560C2×D4—2921no—
561C2×D4—1462no—
562C2×D4—1462no—
563C2×D4—1462no—
564C2×D4—1462no—
565C2×D4—1462no—
566C2×D4—1462no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—2921no—
572C22×C4—2921no—
573C22×C4—731no—
574C22×C4—731no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—731no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4C2×C4×D7311yescharacteristic
596C22×C4C2×C4×D7311yescharacteristic
597C22×C4C2×C4×D7311yescharacteristic
598C22×C4C2×C4×D7311yescharacteristic
599C22×C4C2×C4×D7311yescharacteristic
600C22×C4C2×C22⋊D7312yes—
601C22×C4C2×D29212yes—
602C22×C4C23×D7311yescharacteristic
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8—1461no—
618C2×C8—1461no—
619C2×C8—1461no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C4⋊C4—1462no—
630C4⋊C4—1462no—
631C4⋊C4—1462no—
632C4⋊C4—1462no—
633C4⋊C4—1462no—
634C4⋊C4—1462no—
635C4⋊C4—1462no—
636C4⋊C4—1462no—
637C4⋊C4#1192400514yes—
638C4⋊C4#1192400514yes—
639C22⋊C4—1462no—
640C22⋊C4—1462no—
641C22⋊C4—1462no—
642C22⋊C4—1462no—
643C22⋊C4—1462no—
644C22⋊C4—1462no—
645C22⋊C4—1462no—
646C22⋊C4—1462no—
647C22⋊C4#1192400514yes—
648C22⋊C4#1192400514yes—
649C42—1462no—
650C42—1462no—
651C42—1461no—
652C42—1461no—
653C42—1461no—
654C42—1461no—
655C42C2×C22⋊D7312yes—
656C42C2×C22⋊D7312yes—
657C42C2×D29212yes—
658C42C2×D29212yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—732no—
666C23—1461no—
667C23—1461no—
668C23—1461no—
669C23—1461no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23C2×#1192400512yes—
680C23C22×C4×D7311yescharacteristic
681Q8—2924no—
682D4—2924no—
683D4—2924no—
684D4—2924no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—2924no—
700C2×C4—2924no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—2921no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—732no—
710C2×C4—1461no—
711C2×C4—1461no—
712C2×C4—1461no—
713C2×C4—1461no—
714C2×C4—1461no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1461no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1461no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4C2×#1192400512yes—
728C2×C4C2×#1192400512yes—
729C2×C4C2×#1192400512yes—
730C2×C4C2×#1192400512yes—
731C2×C4C2×#1192400512yes—
732C2×C4C22×C22⋊D7311yescharacteristic
733C2×C4C22×D29211yescharacteristic
734C2×C4#1455663611yescharacteristic
735C2×C4#1455663611yescharacteristic
736C2×C4#1455663911yescharacteristic
737C2×C4#1455663911yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—2921no—
743C8—2921no—
744C8—2921no—
745C8—2921no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—2921no—
754C22—2921no—
755C22—2921no—
756C22—2921no—
757C22—2921no—
758C22—2921no—
759C22—2921no—
760C22—2921no—
761C22—2921no—
762C22—2921no—
763C22—2921no—
764C22—1462no—
765C22—1462no—
766C22—1462no—
767C22C22×#1192400511yescharacteristic
768C22#1798906811yescharacteristic
769C22#1798906811yescharacteristic
770C22#131×D7311yescharacteristic
771C22#131×D7311yescharacteristic
772C22#1798935211yescharacteristic
773C22#1798935211yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—2921no—
780C4—2921no—
781C4—2921no—
782C4—2921no—
783C4—2921no—
784C4—1462no—
785C4#1798915411yescharacteristic
786C4#1798916111yescharacteristic
787C4#1798916811yescharacteristic
788C4#1798916811yescharacteristic
789C2—42no—
790C2—2922no—
791C2—5841no—
792C2#2261252411yescharacteristic
793C2#2261837811yescharacteristic
794C2#2261837811yescharacteristic
795C2#2261906811yescharacteristic
796C2#2261907811yescharacteristic
797C2#2261908911yescharacteristic
798C2#2261909911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#424×C73C2
prime radicalC2×#14556564C4
cosocleC22×C4×C73C24
hypercenterC2×#424D73
hypocenterC73#21855
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#17988648C2semidirect
3. #22610870C2semidirect
4. #22610866C2semidirect
5. #22610728C2semidirect
6. #22610724C2semidirect
7. #22610228C2semidirect
8. #22610228C2semidirect
9. #22610223C2semidirect
10. #22610223C2semidirect
11. #22609912C2semidirect
12. #22609912C2semidirect
13. #22609908C2semidirect
14. #22609908C2semidirect
15. C2×#424×C73C2semidirect
402. C2×#424D73semidirect
415. C73#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#179891152
C2×#179886482
#226108702
#226108662
#226107282
#226107242
#226102282
#226102232
#226099122
#226099082
C2×#424×C732
#2185573