Finite Group Databasebeta

← #33106372

Subgroups — #33106372

Order 18688.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988732C211yesmaximal, characteristic
2C2×#17988685C211yesmaximal, characteristic, complemented
3C2×#17988588C211yesmaximal, characteristic, complemented
4#22612945C211yesmaximal, characteristic, complemented
5#22610796C211yesmaximal, characteristic, complemented
6#22610631C211yesmaximal, characteristic, complemented
7#22610548C211yesmaximal, characteristic, complemented
8#22610367C211yesmaximal, characteristic, complemented
9#22610286C211yesmaximal, characteristic, complemented
10#22610282C211yesmaximal, characteristic, complemented
11#22610185C211yesmaximal, characteristic, complemented
12#22610118C211yesmaximal, characteristic, complemented
13C4×#14556515C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15C73×#2341C211yesmaximal, characteristic, complemented
16C22×#11924015C2211yescharacteristic
17C22×#11924013C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C2×#14556565C2211yescharacteristic
20C2×C4×D292C2211yescharacteristic
21C2×#14556551—21no—
22C22×C4⋊Dic73C2211yescharacteristic
23#17988732C418yescomplemented
24#17988685—24no—
25C2×#14556524C2211yescharacteristic
26C2×#14556524C2211yescharacteristic
27#17988588—24no—
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×#14556515C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556511C2211yescharacteristic
35C2×#14556511C2211yescharacteristic
36C2×C22⋊#10596831C2211yescharacteristic
37C2×#14556502C2211yescharacteristic
38C2×C4×#10596831C2211yescharacteristic
39#17988489C2211yescharacteristic
40#17988485C2211yescharacteristic
41#17988479—21no—
42#17988464—21no—
43#17988461—21no—
44C4×C4⋊Dic73C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C22×#41×C73C2211yescharacteristic
52C2×C4×Q8×C73C2211yescharacteristic
53C2×C4×Q8×C73C2211yescharacteristic
54#390×C73—21no—
55#390×C73—21no—
56#390×C73C2211yescharacteristic
57#390×C73C2211yescharacteristic
58#380×C73—21no—
59#380×C73C2211yescharacteristic
60C4×C22⋊C4×C73—21no—
61C4×C22⋊C4×C73C2211yescharacteristic
62C22×D292C2311yescharacteristic
63C22×C22⋊D73—21no—
64C23×Dic73—21no—
65C22×C4×D73—21no—
66C2×#11924015—22no—
67C2×#11924015—22no—
68C2×#11924015C2×C414yescomplemented
69C2×#11924013—41no—
70C2×#11924013—41no—
71C2×#11924013C2×C414yescomplemented
72C2×#11924012—22no—
73C2×#11924012—22no—
74C2×#11924012—41no—
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79#14556565—22no—
80#14556565C2×C414yes—
81C4×D292—22no—
82C4×D292—41no—
83#14556551—44no—
84C2×C4⋊Dic73—22no—
85C2×C4⋊Dic73—21no—
86C2×C4⋊Dic73—41no—
87C2×C4⋊Dic73C2311yescharacteristic
88C2×C4⋊Dic73C2311yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×#11924007—21no—
91C2×#11924005—21no—
92C2×#11924005—21no—
93C2×#11924005—21no—
94C2×#11924005—21no—
95C2×C4×Dic73—21no—
96#14556524—22no—
97#14556524—41no—
98#14556515—22no—
99#14556515C2×C414yescomplemented
100#14556515D414yescomplemented
101#14556512—22no—
102#14556512—22no—
103#14556512C2×C414yescomplemented
104#14556511—22no—
105#14556511—41no—
106C22⋊#10596831C2×C414yescomplemented
107#14556502—22no—
108C4×#10596831—41no—
109#14556498—21no—
110#14556498—21no—
111C2×#41×C73—22no—
112C2×#41×C73—22no—
113C2×#41×C73—22no—
114C2×#41×C73—41no—
115C2×#41×C73—41no—
116C2×#41×C73C2×C414yescomplemented
117C22×Q8×C73C2311yescharacteristic
118C22×D4×C73—21no—
119C22×D4×C73C2311yescharacteristic
120C23×C4×C73—21no—
121C23×C4×C73C2311yescharacteristic
122C4×Q8×C73—22no—
123C4×Q8×C73—22no—
124C4×Q8×C73—41no—
125C4×Q8×C73—41no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73—21no—
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C4⋊C4×C73C2311yescharacteristic
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C22⋊C4×C73D411yescharacteristic
137C2×C42×C73—21no—
138C2×C42×C73—21no—
139C2×C42×C73C2311yescharacteristic
140C2×C42×C73C2311yescharacteristic
141#95×C73—21no—
142#95×C73D411yescharacteristic
143#95×C73D411yescharacteristic
144C23×D73—21no—
145C2×D292—21no—
146C2×D292—21no—
147C2×D292—21no—
148C2×D292—21no—
149C2×D292—21no—
150C2×D292C22×C412yes—
151C2×C22⋊D73—24no—
152C2×C22⋊D73—42no—
153C2×C22⋊D73—42no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—42no—
158C22×Dic73—42no—
159C22×Dic73—81no—
160C2×C4×D73—42no—
161C2×C4×D73—42no—
162C2×C4×D73—81no—
163#11924015—28no—
164#11924013—44no—
165#11924012—44no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831C22×C412yes—
176C2×#10596831C22×C412yes—
177C2×#10596831C2×D412yes—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73—42no—
183C4⋊Dic73C22×C412yes—
184C4⋊Dic73C2×D412yes—
185#11924007—42no—
186#11924005—24no—
187#11924005—42no—
188#11924005—42no—
189#11924005—81no—
190C4×Dic73—42no—
191C24×C73—21no—
192C24×C73C2×D411yescharacteristic
193#41×C73—28no—
194#41×C73—44no—
195#41×C73—44no—
196#41×C73—44no—
197C2×Q8×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73C22×C412yes—
201C2×Q8×C73C2×D412yes—
202C2×Q8×C73#4112yes—
203C2×D4×C73—24no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—21no—
209C2×D4×C73—42no—
210C2×D4×C73—42no—
211C2×D4×C73C22×C412yes—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—24no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—42no—
221C22×C4×C73—42no—
222C22×C4×C73C22×C412yes—
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73C2×D411yescharacteristic
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73#4112yes—
229C22×C4×C73C2411yescharacteristic
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—42no—
235C4⋊C4×C73—42no—
236C22⋊C4×C73—22no—
237C22⋊C4×C73—41no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—81no—
241C22⋊C4×C73—81no—
242C22⋊C4×C73—81no—
243C42×C73—21no—
244C42×C73—21no—
245C42×C73—21no—
246C42×C73—21no—
247C42×C73—42no—
248C42×C73—42no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—22no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73C4×D412yes—
263C23×C73C22×D411yescharacteristic
264C22×D73—22no—
265C22×D73—41no—
266C22×D73—41no—
267C22×D73—41no—
268C22×D73—41no—
269C22×D73—41no—
270C22×D73—41no—
271Q8×C73—22no—
272Q8×C73—22no—
273Q8×C73—22no—
274Q8×C73C4×D414yescomplemented
275D4×C73—22no—
276D4×C73—22no—
277D4×C73—48no—
278D4×C73—41no—
279D4×C73—41no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—22no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—48no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73C4×D412yes—
308C2×C4×C73AGL(1,ℤ/8)12yes—
309C2×C4×C73C23×C411yescharacteristic
310C2×C4×C73C22×D411yescharacteristic
311C2×C4×C73C2×#4111yescharacteristic
312C2×C4×C73C2×#4111yescharacteristic
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C2×C4×C73H(5,𝔽2)11yescharacteristic
315C22⋊D73—48no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73—41no—
322C2×Dic73—41no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—84no—
326D292—22no—
327D292—22no—
328D292—41no—
329D292—41no—
330C4×D73—84no—
331#10596831—22no—
332#10596831—22no—
333#10596831—22no—
334#10596831—41no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73—81no—
349C22×C73C2×C4×D411yescharacteristic
350C22×C73D4211yescharacteristic
351C22×C73#54611yescharacteristic
352C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C73#57511yescharacteristic
354C22×C73#57611yescharacteristic
355C22×C73#57811yescharacteristic
356C2×D73—42no—
357C2×D73—42no—
358C2×D73—42no—
359C2×D73—81no—
360C2×D73—81no—
361C2×D73—81no—
362C2×D73—81no—
363C4×C73—22no—
364C4×C73—24no—
365C4×C73—22no—
366C4×C73—41no—
367C4×C73—41no—
368C4×C73—41no—
369C4×C73—81no—
370C4×C73—81no—
371C4×C73C2×C4×D411yescharacteristic
372C4×C73#51811yescharacteristic
373C4×C73#54611yescharacteristic
374C4×C73#55111yescharacteristic
375Dic73—42no—
376Dic73—42no—
377Dic73—81no—
378#22863—731nomaximal, Sylow
379C2×C73—42no—
380C2×C73—82no—
381C2×C73#235811yescharacteristic
382C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C73#295111yescharacteristic
384C2×C73#327411yescharacteristic
385C2×C73#327711yescharacteristic
386C2×C73#330811yescharacteristic
387C2×C73#330911yescharacteristic
388D73—82no—
389C2×#449—731no—
390C2×#440—731no—
391C2×#417—731no—
392#2361—731no—
393#2341D7311yescharacteristic, complemented
394#1970—731no—
395#1936—731no—
396#1925—731no—
397#1895—731no—
398#1880—731no—
399#1879—731no—
400#1863—731no—
401#1852—731no—
402C4×#103—731no—
403#1753—731no—
404C73#2286311yescharacteristic, complemented, Sylow
405C22×#41C2×D7311yescharacteristic
406C22×SD16—731no—
407C22×D8—731no—
408C22×M16—731no—
409C2×#121—731no—
410C2×C4×Q8C2×D7311yescharacteristic
411C2×C4×Q8C2×D7311yescharacteristic
412C2×C4×D4—731no—
413C2×C4×D4—1461no—
414C22×C4⋊C4—731no—
415#449—738no—
416#440—1464no—
417C2×#107—731no—
418C2×#107—731no—
419#417—1464no—
420C2×#103—731no—
421C2×#103—731no—
422C2×#103—731no—
423C2×#102—731no—
424C2×#102—731no—
425C2×#102—731no—
426C2×#102—731no—
427C2×#102—731no—
428C2×C22⋊C8—731no—
429C2×#97—731no—
430C2×C4×C8—731no—
431#390—21no—
432#390—21no—
433#390—731no—
434#390C2×D7311yescharacteristic
435#390C2×D7311yescharacteristic
436#389—731no—
437#388—1461no—
438#386—1461no—
439#385—1461no—
440#380—21no—
441#380C2×D7311yescharacteristic
442C4×C4⋊C4—731no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2×D7311yescharacteristic
445#340—731no—
446#340—731no—
447#340—731no—
448#340—731no—
449#336—731no—
450#336—731no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C4×D7314yescomplemented
457C22×Q8C22×D7311yescharacteristic
458C22×D4—21no—
459C22×D4—731no—
460C22×D4—1461no—
461C22×D4C22×D7311yescharacteristic
462C23×C4—21no—
463C23×C4—1461no—
464C23×C4—1461no—
465C23×C4C22×D7311yescharacteristic
466C2×SD16—734no—
467C2×SD16—1462no—
468C2×SD16—1462no—
469C2×D8—2921no—
470C2×D8—2921no—
471C2×D8—734no—
472C2×M16—2921no—
473C2×M16—1462no—
474C2×M16—1462no—
475C22×C8—731no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—731no—
479#121—734no—
480#121—1462no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—41no—
484C4×Q8—41no—
485C4×D4—2921no—
486C4×D4—2924no—
487C4×D4—1462no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—2921no—
491C2×C4⋊C4—731no—
492C2×C4⋊C4—731no—
493C2×C4⋊C4—731no—
494C2×C4⋊C4—1461no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1462no—
497C2×C4⋊C4C22×D7311yescharacteristic
498C2×C4⋊C4C22×D7311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1461no—
505C2×C22⋊C4—1461no—
506C2×C22⋊C4—1461no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4C22⋊D7311yescharacteristic
509C2×C22⋊C4C22⋊D7311yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—1461no—
513C2×C42C22×D7311yescharacteristic
514C2×C42C22×D7311yescharacteristic
515#107—2921no—
516#107—1462no—
517#103—734no—
518#103—734no—
519#103—1462no—
520#102—2921no—
521#102—734no—
522#102—1462no—
523#102—1462no—
524#102—1462no—
525C22⋊C8—734no—
526#97—1462no—
527C4×C8—2921no—
528#95—21no—
529#95—1461no—
530#95—1461no—
531#95C22⋊D7311yescharacteristic
532#95C22⋊D7311yescharacteristic
533C24—21no—
534C24—1461no—
535C24C2×C22⋊D7311yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C4×D7312yes—
544C2×Q8D4×D7312yes—
545C2×Q8#1192402712yes—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—2922no—
555C2×D4—2922no—
556C2×D4—732no—
557C2×D4—1464no—
558C2×D4—1461no—
559C2×D4—1461no—
560C2×D4—1461no—
561C2×D4—1461no—
562C2×D4—1461no—
563C2×D4C2×C4×D7312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—2922no—
575C22×C4—2922no—
576C22×C4—2922no—
577C22×C4—2922no—
578C22×C4—5841no—
579C22×C4—5841no—
580C22×C4—1461no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4C2×C4×D7312yes—
584C22×C4C2×C22⋊D7311yescharacteristic
585C22×C4C2×C22⋊D7311yescharacteristic
586C22×C4C2×C22⋊D7311yescharacteristic
587C22×C4C2×C22⋊D7311yescharacteristic
588C22×C4C2×C22⋊D7311yescharacteristic
589C22×C4#1192402812yes—
590C22×C4C23×D7311yescharacteristic
591SD16—1468no—
592D8—2924no—
593M16—2924no—
594C2×C8—732no—
595C2×C8—732no—
596C2×C8—732no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8—1461no—
600C2×C8—1461no—
601C2×C8—1461no—
602C2×C8—1461no—
603C2×C8—1461no—
604C2×C8—1461no—
605C2×C8—1461no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—2922no—
613C4⋊C4—2922no—
614C4⋊C4—732no—
615C4⋊C4—732no—
616C4⋊C4—1461no—
617C4⋊C4—1461no—
618C4⋊C4—1461no—
619C4⋊C4—1461no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—2922no—
628C22⋊C4—2922no—
629C22⋊C4—5841no—
630C22⋊C4—1464no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—42no—
637C42—2922no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—2921no—
652C23—2921no—
653C23—2921no—
654C23—2921no—
655C23—2921no—
656C23—2921no—
657C23—1462no—
658C23C4×C22⋊D7312yes—
659C23C22×C22⋊D7311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8#1455655114yescomplemented
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—2928no—
670D4—2921no—
671D4—2921no—
672D4—1462no—
673D4—1462no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
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—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—2921no—
707C2×C4—2921no—
708C2×C4—5844no—
709C2×C4—5844no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4C4×C22⋊D7312yes—
713C2×C4#1455661612yes—
714C2×C4C22×C4×D7311yescharacteristic
715C2×C4C2×D4×D7311yescharacteristic
716C2×C4C2×#1192402711yescharacteristic
717C2×C4C2×#1192402811yescharacteristic
718C2×C4#1455663611yescharacteristic
719C2×C4#1455663611yescharacteristic
720C8—2921no—
721C8—1462no—
722C8—1462no—
723C8—1462no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—2922no—
739C22—2922no—
740C22—2922no—
741C22—5841no—
742C22—5841no—
743C22—5841no—
744C22—5841no—
745C22C2×C4×C22⋊D7311yescharacteristic
746C22D4×C22⋊D7311yescharacteristic
747C22#1798923111yescharacteristic
748C22C2×#1455661611yescharacteristic
749C22#1798938511yescharacteristic
750C22#1798939011yescharacteristic
751C22#1798940211yescharacteristic
752C4—22no—
753C4—24no—
754C4—22no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—2922no—
761C4—2922no—
762C4—5841no—
763C4C2×#1455655111yescharacteristic
764C4#1798906011yescharacteristic
765C4#1798922711yescharacteristic
766C4#1798926311yescharacteristic
767C2—42no—
768C2—82no—
769C2—5842no—
770C2#2261291011yescharacteristic
771C2C4×#1455661611yescharacteristic
772C2#2261880411yescharacteristic
773C2#2262155111yescharacteristic
774C2#2262158411yescharacteristic
775C2#2262192211yescharacteristic
776C2#2262193711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2341C2
socleC23×C73C22×D4
prime radicalC2×#17988732C2
cosocleC22×C4×C73C24
hypercenter#2341D73
hypocenterC73#22863
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#17988685C2semidirect
3. C2×#17988588C2semidirect
4. #22612945C2semidirect
5. #22610796C2semidirect
6. #22610631C2semidirect
7. #22610548C2semidirect
8. #22610367C2semidirect
9. #22610286C2semidirect
10. #22610282C2semidirect
11. #22610185C2semidirect
12. #22610118C2semidirect
13. C4×#14556515C2semidirect
14. #22609715C2semidirect
15. C73×#2341C2semidirect
23. #17988732C4semidirect
68. C2×#11924015C2×C4semidirect
71. C2×#11924013C2×C4semidirect
99. #14556515C2×C4semidirect
100. #14556515D4semidirect
103. #14556512C2×C4semidirect
106. C22⋊#10596831C2×C4semidirect
116. C2×#41×C73C2×C4semidirect
274. Q8×C73C4×D4semidirect
393. #2341D73semidirect
404. C73#22863semidirect
456. C2×#41C4×D73semidirect
663. Q8#14556551semidirect

Maximal subgroups

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

subgroupindex
C2×#179887322
C2×#179886852
C2×#179885882
#226129452
#226107962
#226106312
#226105482
#226103672
#226102862
#226102822
#226101852
#226101182
C4×#145565152
#226097152
C73×#23412
#2286373