Finite Group Databasebeta

← #33102220

Subgroups — #33102220

Order 18688.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989292C211yesmaximal, characteristic
2C2×C8×C22⋊D73C211yesmaximal, characteristic
3C4⋊C4×C22⋊D73C211yesmaximal, characteristic
4#22610890C211yesmaximal, characteristic, complemented
5#22610877C211yesmaximal, characteristic, complemented
6#22610354C211yesmaximal, characteristic, complemented
7#22610353C211yesmaximal, characteristic, complemented
8#22610238C211yesmaximal, characteristic, complemented
9#22610237C211yesmaximal, characteristic, complemented
10#22610021C211yesmaximal, characteristic, complemented
11#22610020C211yesmaximal, characteristic, complemented
12#22609935C211yesmaximal, characteristic, complemented
13#22609750C211yesmaximal, characteristic, complemented
14#340×D73C211yesmaximal, characteristic, complemented
15C2×#340×C73C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17#17989292—24no—
18#17989292C418yescomplemented
19C2×#14556590C2211yescharacteristic
20C2×#14556581—21no—
21C2×#14556571C2211yescharacteristic
22C2×#14556570—21no—
23C2×#14556570C2211yescharacteristic
24C2×#14556569—21no—
25C2×#14556556C2211yescharacteristic
26C2×C4×C22⋊D73—21no—
27C2×C4×C22⋊D73—21no—
28C2×C4×C22⋊D73C2211yescharacteristic
29C2×C4⋊C4×D73C2211yescharacteristic
30C2×C4⋊C4×D73C2211yescharacteristic
31C8×C22⋊D73—24no—
32C2×#14556520C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34C2×#14556516C2211yescharacteristic
35C2×#14556514C2211yescharacteristic
36C2×#14556514C2211yescharacteristic
37C2×C22⋊#10596831C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×C8×Dic73C2211yescharacteristic
40#17988482—21no—
41#17988460—21no—
42#17988458—21no—
43#17988456C2211yescharacteristic
44#17988447C2211yescharacteristic
45#17988444C2211yescharacteristic
46C4⋊C4×Dic73C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C23×C8×C73C2211yescharacteristic
56C22×C4⋊C4×C73C2211yescharacteristic
57C22×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×Dic146C2311yescharacteristic
64C22×C22⋊D73D411yescharacteristic
65C22×C4×D73—21no—
66C22×C4×D73—21no—
67C22×C4×D73C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C8×D73—22no—
71C2×C8×D73—22no—
72C2×C8×D73—41no—
73#14556590—22no—
74#14556590C2×C414yescomplemented
75#14556581—28no—
76#14556571—22no—
77#14556571C2×C414yescomplemented
78#14556570—28no—
79#14556570—22no—
80#14556570C2×C414yescomplemented
81#14556569—28no—
82#14556556—22no—
83#14556556C2×C414yescomplemented
84C4×C22⋊D73—28no—
85C4×C22⋊D73—44no—
86C4×C22⋊D73C2×C414yes—
87C4×C22⋊D73D414yes—
88C2×C4⋊Dic73—21no—
89C2×C4⋊Dic73C2311yescharacteristic
90C2×C4⋊Dic73C2311yescharacteristic
91C2×C4⋊Dic73C2311yescharacteristic
92C2×#11924007—21no—
93C2×#11924007—21no—
94C2×#11924007—21no—
95C2×#11924007—21no—
96C2×#11924007—21no—
97C2×#11924007—21no—
98C2×#11924007—21no—
99C2×#11924007D411yescharacteristic
100C4⋊C4×D73—22no—
101C4⋊C4×D73—22no—
102C4⋊C4×D73—41no—
103C4⋊C4×D73C2×C414yescomplemented
104C2×C22⋊Dic73—21no—
105C2×C22⋊Dic73—21no—
106C2×C22⋊Dic73D411yescharacteristic
107C2×#11924005—21no—
108C2×#11924005—21no—
109C2×#11924005D411yescharacteristic
110C2×C4×Dic73—21no—
111C2×C4×Dic73—21no—
112C2×C4×Dic73C2311yescharacteristic
113#14556520—22no—
114#14556516—22no—
115#14556516—41no—
116#14556514—22no—
117#14556514—41no—
118C22⋊#10596831—22no—
119#14556503—22no—
120C8×Dic73—22no—
121#14556498—21no—
122#14556498—21no—
123#14556498—21no—
124C23×C4×C73—21no—
125C23×C4×C73—21no—
126C23×C4×C73C2311yescharacteristic
127C22×C8×C73—22no—
128C22×C8×C73—22no—
129C22×C8×C73—41no—
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C2×C4⋊C4×C73—22no—
133C2×C4⋊C4×C73—21no—
134C2×C4⋊C4×C73—22no—
135C2×C4⋊C4×C73—21no—
136C2×C4⋊C4×C73—41no—
137C2×C4⋊C4×C73C2×C414yescomplemented
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C4⋊C4×C73C2311yescharacteristic
141C2×C4⋊C4×C73C2311yescharacteristic
142C23×D73C2×D411yescharacteristic
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146—24no—
149C2×Dic146—81no—
150C2×Dic146—81no—
151C2×Dic146C22×C412yes—
152C2×C22⋊D73C22⋊C414yes—
153C2×C22⋊D73SD1614yes—
154C2×C22⋊D73Q1614yes—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73C2×D411yescharacteristic
160C22×Dic73C2×D411yescharacteristic
161C22×Dic73C2×D411yescharacteristic
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—24no—
167C2×C4×D73—42no—
168C2×C4×D73—42no—
169C2×C4×D73—81no—
170C2×C4×D73—81no—
171C2×C4×D73—81no—
172C2×C4×D73C22×C412yes—
173C2×C4×D73C2×D412yes—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C8×D73—44no—
181C4⋊Dic73—21no—
182C4⋊Dic73—24no—
183C4⋊Dic73—21no—
184C4⋊Dic73—21no—
185C4⋊Dic73—21no—
186C4⋊Dic73—21no—
187C4⋊Dic73C22×C412yes—
188#11924007—24no—
189#11924007—24no—
190#11924007—24no—
191#11924007—24no—
192#11924007—42no—
193#11924007—42no—
194#11924007—81no—
195#11924007C22⋊C414yes—
196C22⋊Dic73—24no—
197C22⋊Dic73—42no—
198C22⋊Dic73C22⋊C414yes—
199#11924005—24no—
200#11924005—42no—
201#11924005C22⋊C414yes—
202C4×Dic73—24no—
203C4×Dic73—42no—
204C4×Dic73C22×C412yes—
205C4×Dic73C2×D412yes—
206C24×C73C2×D411yescharacteristic
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—24no—
215C22×C4×C73—21no—
216C22×C4×C73—42no—
217C22×C4×C73—42no—
218C22×C4×C73—81no—
219C22×C4×C73—81no—
220C22×C4×C73—81no—
221C22×C4×C73C22×C412yes—
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D412yes—
224C22×C4×C73C2411yescharacteristic
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—44no—
231C2×C8×C73#4112yes—
232C4⋊C4×C73—24no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—42no—
239C4⋊C4×C73C22×C412yes—
240C4⋊C4×C73C22×C412yes—
241C4⋊C4×C73#4112yes—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73C2×C22⋊C412yes—
247C23×C73C2×SD1612yes—
248C23×C73C2×Q1612yes—
249C23×C73C22×D411yescharacteristic
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73—21no—
254C22×D73C2×C22⋊C412yes—
255C22×D73C2×SD1612yes—
256C22×D73C2×Q1612yes—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—84no—
276C2×C4×C73—84no—
277C2×C4×C73C2×C22⋊C412yes—
278C2×C4×C73C23×C411yescharacteristic
279C2×C4×C73C22×D411yescharacteristic
280C2×C4×C73C2×#4111yescharacteristic
281C2×C4×C73C2×#4111yescharacteristic
282C2×C4×C73H(5,𝔽2)11yescharacteristic
283C2×C4×C732−1+411yescharacteristic
284C22⋊D73#103116yescomplemented
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—22no—
290C2×Dic73—22no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73C2×C22⋊C412yes—
302C2×Dic73C2×C22⋊C412yes—
303C2×Dic73C2×C22⋊C412yes—
304C2×Dic73C2×SD1612yes—
305C2×Dic73C2×Q1612yes—
306C4×D73—22no—
307C4×D73—22no—
308C4×D73—22no—
309C4×D73—22no—
310C4×D73—84no—
311C4×D73—84no—
312Dic146—22no—
313Dic146—22no—
314Dic146—41no—
315Dic146—41no—
316Dic146—84no—
317C8×C73—22no—
318C8×C73—41no—
319#10596831—41no—
320#10596831—41no—
321C22×C73—22no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73C2×#10314yes—
328C22×C73C22×C22⋊C411yescharacteristic
329C22×C73#54611yescharacteristic
330C22×C73#54711yescharacteristic
331C22×C73C22×SD1611yescharacteristic
332C22×C73C22×Q1611yescharacteristic
333C22×C73#57611yescharacteristic
334C22×C73#57711yescharacteristic
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—22no—
338C2×D73—22no—
339C2×D73—22no—
340C2×D73—22no—
341C2×D73C2×#10314yes—
342C4×C73—22no—
343C4×C73—42no—
344C4×C73—42no—
345C4×C73—42no—
346C4×C73—81no—
347C4×C73C4×#4111yescharacteristic
348C4×C73#52011yescharacteristic
349C4×C73#54611yescharacteristic
350C4×C73#54711yescharacteristic
351Dic73—22no—
352Dic73—22no—
353Dic73—42no—
354Dic73—42no—
355Dic73—81no—
356Dic73—81no—
357Dic73C2×#10314yes—
358#22487—731nomaximal, Sylow
359C2×C73—24no—
360C2×C73#233911yescharacteristic
361C2×C73C22×#10311yescharacteristic
362C2×C73#289711yescharacteristic
363C2×C73#329511yescharacteristic
364C2×C73#329911yescharacteristic
365C2×C73#333511yescharacteristic
366C2×C73#333811yescharacteristic
367D73—24no—
368C2×#554—731no—
369C2×C8×D4—731no—
370D4×C4⋊C4—731no—
371#1990—731no—
372#1987—731no—
373#1892—731no—
374#1892—731no—
375#1872—731no—
376#1872—731no—
377#1824—731no—
378#1824—731no—
379#1803—731no—
380C4×#103—731no—
381C2×#340—731no—
382C2×#340D7311yescharacteristic, complemented
383C73#2248711yescharacteristic, complemented, Sylow
384C23×C8—731no—
385C23×C8C2×D7311yescharacteristic
386#554—738no—
387#554—1464no—
388C2×C4⋊Q8—731no—
389C2×#125—1461no—
390C2×C22⋊Q8—731no—
391C2×C22⋊Q8—731no—
392C2×C22⋊Q8—1461no—
393C2×C22⋊Q8—1461no—
394C2×C4×Q8—731no—
395C2×C4×D4—731no—
396C2×C4×D4—1461no—
397C2×C4×D4—1461no—
398C22×C4⋊C4—731no—
399C22×C4⋊C4—731no—
400C22×C4⋊C4C2×D7311yescharacteristic
401C22×C4⋊C4C2×D7311yescharacteristic
402C8×D4—1464no—
403C2×C4⋊C8—731no—
404C2×#103—731no—
405C2×#103—731no—
406C2×#103—731no—
407C2×#103—731no—
408C2×C22⋊C8—731no—
409C2×C22⋊C8—731no—
410C2×C4×C8—731no—
411#389—1461no—
412#385—1461no—
413#385—1461no—
414#384—731no—
415#380—731no—
416#380—731no—
417C4×C4⋊C4—731no—
418#340—731no—
419#340—731no—
420#340—731no—
421#340—731no—
422#340—731no—
423#340—731no—
424#340—731no—
425#340—731no—
426#340C2×D7311yescharacteristic
427#340C2×D7311yescharacteristic
428#340C2×D7311yescharacteristic
429#340C2×D7311yescharacteristic
430C22×Q8—731no—
431C22×Q8—1461no—
432C22×D4—731no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—731no—
436C23×C4—1461no—
437C23×C4—1461no—
438C23×C4C22×D7311yescharacteristic
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8—2921no—
443C22×C8—731no—
444C22×C8—731no—
445C22×C8—1462no—
446C22×C8—1462no—
447C22×C8C22×D7311yescharacteristic
448C22×C8C22×D7311yescharacteristic
449C4⋊Q8—734no—
450C4⋊Q8—1462no—
451#125—1468no—
452C22⋊Q8—734no—
453C22⋊Q8—734no—
454C22⋊Q8—1468no—
455C22⋊Q8—1468no—
456C22⋊Q8—1462no—
457C22⋊Q8—1462no—
458C4×Q8—734no—
459C4×Q8—1462no—
460C4×D4—2924no—
461C4×D4—734no—
462C4×D4—734no—
463C4×D4—1468no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—2921no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4—734no—
473C2×C4⋊C4—731no—
474C2×C4⋊C4—731no—
475C2×C4⋊C4—1462no—
476C2×C4⋊C4—1461no—
477C2×C4⋊C4—1461no—
478C2×C4⋊C4—1462no—
479C2×C4⋊C4—1461no—
480C2×C4⋊C4—1461no—
481C2×C4⋊C4—1461no—
482C2×C4⋊C4—1461no—
483C2×C4⋊C4—1461no—
484C2×C4⋊C4—1461no—
485C2×C4⋊C4C4×D7314yescomplemented
486C2×C4⋊C4C22×D7311yescharacteristic
487C2×C4⋊C4C22×D7311yescharacteristic
488C2×C4⋊C4C22×D7311yescharacteristic
489C2×C4⋊C4C22×D7311yescharacteristic
490C2×C22⋊C4—731no—
491C2×C22⋊C4—731no—
492C2×C22⋊C4—1461no—
493C2×C22⋊C4—1461no—
494C2×C22⋊C4—1461no—
495C2×C22⋊C4—1461no—
496C2×C42—731no—
497C2×C42—1461no—
498C2×C42—1461no—
499C4⋊C8—1462no—
500#103—2921no—
501#103—2921no—
502#103—1462no—
503#103—1462no—
504C22⋊C8—1462no—
505C22⋊C8—1462no—
506C4×C8—1462no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510C24—731no—
511C24D4×D7311yescharacteristic
512C2×Q8—5841no—
513C2×Q8—5841no—
514C2×Q8—732no—
515C2×Q8—1464no—
516C2×Q8—1461no—
517C2×Q8—1461no—
518C2×Q8—1461no—
519C2×Q8—1461no—
520C2×Q8—1461no—
521C2×D4—734no—
522C2×D4—734no—
523C2×D4—734no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—2922no—
539C22×C4—2922no—
540C22×C4—5841no—
541C22×C4—5841no—
542C22×C4—5841no—
543C22×C4—731no—
544C22×C4—731no—
545C22×C4—731no—
546C22×C4—732no—
547C22×C4—732no—
548C22×C4—1464no—
549C22×C4—1461no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4C2×C4×D7312yes—
558C22×C4D4×D7311yescharacteristic
559C22×C4D4×D7312yes—
560C22×C4C23×D7311yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—44no—
567C2×C8—2924no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8#1192402812yes—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—2922no—
583C4⋊C4—2922no—
584C4⋊C4—5841no—
585C4⋊C4—734no—
586C4⋊C4—732no—
587C4⋊C4—1464no—
588C4⋊C4—1464no—
589C4⋊C4—1464no—
590C4⋊C4—1464no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4—1461no—
594C4⋊C4—1461no—
595C4⋊C4—1464no—
596C4⋊C4—1461no—
597C4⋊C4C2×C4×D7312yes—
598C4⋊C4C2×C4×D7312yes—
599C4⋊C4#1192402812yes—
600C22⋊C4—2922no—
601C22⋊C4—2922no—
602C22⋊C4—734no—
603C22⋊C4—734no—
604C22⋊C4—1464no—
605C22⋊C4—1464no—
606C42—2922no—
607C42—732no—
608C42—732no—
609C42—1464no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—732no—
615C23—732no—
616C23—732no—
617C23—1461no—
618C23—1461no—
619C23—1461no—
620C23—1461no—
621C23C22⋊C4×D7312yes—
622C23SD16×D7312yes—
623C23Q16×D7312yes—
624C23C2×D4×D7311yescharacteristic
625Q8—2921no—
626Q8—2921no—
627Q8—5844no—
628Q8—1462no—
629Q8—1462no—
630D4—7316no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—5844no—
662C2×C4—5844no—
663C2×C4—732no—
664C2×C4—732no—
665C2×C4—732no—
666C2×C4—732no—
667C2×C4—732no—
668C2×C4—1462no—
669C2×C4—1462no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4C22⋊C4×D7312yes—
679C2×C4C22×C4×D7311yescharacteristic
680C2×C4C2×D4×D7311yescharacteristic
681C2×C4C2×#1192402811yescharacteristic
682C2×C4C2×#1192402811yescharacteristic
683C2×C4#1455663611yescharacteristic
684C2×C4#1455663911yescharacteristic
685C8—22no—
686C8—41no—
687C8—2921no—
688C8—2921no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—734no—
696C22—1462no—
697C22—1462no—
698C22—1462no—
699C22—1462no—
700C22—1462no—
701C22—1462no—
702C22#103×D7314yes—
703C22C2×C22⋊C4×D7311yescharacteristic
704C22#1798922711yescharacteristic
705C22#1798923811yescharacteristic
706C22C2×SD16×D7311yescharacteristic
707C22C2×Q16×D7311yescharacteristic
708C22#1798938811yescharacteristic
709C22#1798939311yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—2922no—
716C4—2922no—
717C4—5841no—
718C4—5841no—
719C4—734no—
720C4—1462no—
721C4—1462no—
722C4C4×#1192402811yescharacteristic
723C4#1798906811yescharacteristic
724C4#1798922711yescharacteristic
725C4#1798923811yescharacteristic
726C2—24no—
727C2—1464no—
728C2#2261275811yescharacteristic
729C2C2×#103×D7311yescharacteristic
730C2#2261845211yescharacteristic
731C2#2262175111yescharacteristic
732C2#2262180311yescharacteristic
733C2#2262228411yescharacteristic
734C2#2262232111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#340×C73C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
cosocleC22×C4×C73C24
hypercenterC2×#340D73
hypocenterC73#22487
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #22610890C2semidirect
5. #22610877C2semidirect
6. #22610354C2semidirect
7. #22610353C2semidirect
8. #22610238C2semidirect
9. #22610237C2semidirect
10. #22610021C2semidirect
11. #22610020C2semidirect
12. #22609935C2semidirect
13. #22609750C2semidirect
14. #340×D73C2semidirect
15. C2×#340×C73C2semidirect
18. #17989292C4semidirect
74. #14556590C2×C4semidirect
77. #14556571C2×C4semidirect
80. #14556570C2×C4semidirect
83. #14556556C2×C4semidirect
103. C4⋊C4×D73C2×C4semidirect
137. C2×C4⋊C4×C73C2×C4semidirect
284. C22⋊D73#103semidirect
382. C2×#340D73semidirect
383. C73#22487semidirect
485. C2×C4⋊C4C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179892922
C2×C8×C22⋊D732
C4⋊C4×C22⋊D732
#226108902
#226108772
#226103542
#226103532
#226102382
#226102372
#226100212
#226100202
#226099352
#226097502
#340×D732
C2×#340×C732
#2248773