Finite Group Databasebeta

← #33052215

Subgroups — #33052215

Order 18688.

944 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989270C211yesmaximal, characteristic
2#22618589C211yesmaximal, characteristic, complemented
3#22608301C211yesmaximal, characteristic, complemented
4#22608298C211yesmaximal, characteristic, complemented
5#22608288C211yesmaximal, characteristic, complemented
6#22608286C211yesmaximal, characteristic, complemented
7#22608280C211yesmaximal, characteristic
8#22608277C211yesmaximal, characteristic
9#22608274C211yesmaximal, characteristic, complemented
10#22608263C211yesmaximal, characteristic, complemented
11#22608260C211yesmaximal, characteristic, complemented
12#22608254C211yesmaximal, characteristic, complemented
13#22608243C211yesmaximal, characteristic, complemented
14C2×#17988312C211yesmaximal, characteristic, complemented
15C73×#2924C211yesmaximal, characteristic, complemented
16#17989270—21no—
17#17989270—21no—
18#17989270—21no—
19#17989270—21no—
20#17989270—21no—
21#17989270—21no—
22#17989270—21no—
23#17989270—21no—
24C2×#14556586C411yescharacteristic
25C2×#14556585C2211yescharacteristic
26C2×#14556583C2211yescharacteristic
27C2×#14556581C411yescharacteristic
28C2×#14556581C411yescharacteristic
29C2×#14556575C411yescharacteristic
30C2×#14556574C2211yescharacteristic
31C2×#14556569C411yescharacteristic
32C2×#14556568C411yescharacteristic
33C2×C4×Dic146C2211yescharacteristic
34C2×#14556551C411yescharacteristic
35C2×#14556548C2211yescharacteristic
36C2×#14556547C411yescharacteristic
37C22×#11924007C2211yescharacteristic
38#17988648—21no—
39#17988648—21no—
40#17988644C2211yescharacteristic
41#17988644C2211yescharacteristic
42#17988640C2211yescharacteristic
43#17988640C2211yescharacteristic
44#17988614—21no—
45#17988551C2211yescharacteristic
46C2×C22⋊#10596831C2211yescharacteristic
47#17988543—21no—
48#17988312C2211yescharacteristic
49#17988312C2211yescharacteristic
50#17988312C2211yescharacteristic
51#17988312C2211yescharacteristic
52#17988312C2211yescharacteristic
53#17988312C2211yescharacteristic
54#17988312C2211yescharacteristic
55#17988312C2211yescharacteristic
56#17988312C2211yescharacteristic
57#17988312C2211yescharacteristic
58#17988312C2211yescharacteristic
59#17988312C2211yescharacteristic
60#17988310C2211yescharacteristic
61#17988310C2211yescharacteristic
62#17988310C2211yescharacteristic
63#17988310C2211yescharacteristic
64C2×#117×C73C2211yescharacteristic
65#433×C73—21no—
66#433×C73—21no—
67#432×C73C2211yescharacteristic
68#432×C73C2211yescharacteristic
69#431×C73C2211yescharacteristic
70#431×C73C2211yescharacteristic
71#424×C73—21no—
72#407×C73C2211yescharacteristic
73C2×C22⋊C8×C73C2211yescharacteristic
74#405×C73—21no—
75C22×Dic146C2×C411yescharacteristic
76C22×C22⋊D73C2×C411yescharacteristic
77C23×Dic73C2×C411yescharacteristic
78C23×Dic73C2×C411yescharacteristic
79C22×C4×D73C2×C411yescharacteristic
80C2×#11924012—21no—
81C22×#10596831—21no—
82#14556586—21no—
83#14556586—21no—
84#14556586—21no—
85#14556586—21no—
86#14556585—21no—
87#14556585—21no—
88#14556585—21no—
89#14556585—21no—
90#14556583—21no—
91#14556583—21no—
92#14556583—21no—
93#14556583—21no—
94#14556581—21no—
95#14556581—21no—
96#14556581—21no—
97#14556581—21no—
98#14556581—21no—
99#14556581—21no—
100#14556581—21no—
101#14556581—21no—
102#14556575—21no—
103#14556575—21no—
104#14556575—21no—
105#14556575—21no—
106#14556574—21no—
107#14556574—21no—
108#14556574—21no—
109#14556574—21no—
110#14556569—21no—
111#14556569—21no—
112#14556569—21no—
113#14556569—21no—
114#14556568—21no—
115#14556568—21no—
116#14556568—21no—
117#14556568—21no—
118C4×Dic146—21no—
119C4×Dic146—21no—
120C4×Dic146—21no—
121C4×Dic146—21no—
122#14556551—21no—
123#14556551—21no—
124#14556551—21no—
125#14556551—21no—
126#14556548—21no—
127#14556548—21no—
128#14556548—21no—
129#14556548—21no—
130#14556547—21no—
131#14556547—21no—
132#14556547—21no—
133#14556547—21no—
134C2×C4⋊Dic73C2×C411yescharacteristic
135C2×C4⋊Dic73C2×C411yescharacteristic
136C2×C4⋊Dic73C2×C411yescharacteristic
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×#11924007C2×C411yescharacteristic
142C2×#11924007C2×C411yescharacteristic
143C2×#11924007C2×C411yescharacteristic
144C2×#11924007C2×C411yescharacteristic
145C2×#11924007C2×C411yescharacteristic
146C2×#11924007C2×C411yescharacteristic
147C2×#11924007C2×C411yescharacteristic
148C2×#11924007C2×C411yescharacteristic
149C2×#11924007C2311yescharacteristic
150C2×#11924007C2311yescharacteristic
151C2×#11924007C2311yescharacteristic
152C2×C22⋊Dic73C2×C411yescharacteristic
153C2×#11924005C2×C411yescharacteristic
154C2×#11924005C2×C411yescharacteristic
155C2×#11924005C2×C411yescharacteristic
156C2×#11924005C2×C411yescharacteristic
157C2×#11924005C2311yescharacteristic
158C2×C4×Dic73C2×C411yescharacteristic
159C2×C4×Dic73C2×C411yescharacteristic
160C2×C4×Dic73C2×C411yescharacteristic
161C4⋊#10596831—21no—
162C4⋊#10596831—21no—
163C4⋊#10596831—21no—
164C4⋊#10596831—21no—
165C22⋊#10596831—21no—
166C22⋊#10596831—21no—
167C22⋊#10596831C2311yescharacteristic
168C22⋊#10596831C2311yescharacteristic
169C22⋊#10596831C2311yescharacteristic
170C22⋊#10596831C2311yescharacteristic
171#14556502—21no—
172#14556502—21no—
173C4×#10596831—21no—
174C4×#10596831—21no—
175C23×C4×C73C2311yescharacteristic
176C2×M16×C73—21no—
177C22×C8×C73—21no—
178#117×C73D411yescharacteristic
179#117×C73D411yescharacteristic
180#117×C73D411yescharacteristic
181#117×C73D411yescharacteristic
182#117×C73D411yescharacteristic
183#117×C73D411yescharacteristic
184#117×C73D411yescharacteristic
185#117×C73D411yescharacteristic
186C2×C4⋊C4×C73C2×C411yescharacteristic
187C2×C4⋊C4×C73C2×C411yescharacteristic
188C2×C22⋊C4×C73C2×C411yescharacteristic
189C2×C22⋊C4×C73C2×C411yescharacteristic
190C2×C42×C73C2311yescharacteristic
191C2×C42×C73C2311yescharacteristic
192C4⋊C8×C73—21no—
193C4⋊C8×C73—21no—
194C4⋊C8×C73—21no—
195C4⋊C8×C73—21no—
196C22⋊C8×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73C2311yescharacteristic
199C22⋊C8×C73C2311yescharacteristic
200C22⋊C8×C73C2311yescharacteristic
201C22⋊C8×C73C2311yescharacteristic
202#97×C73—21no—
203#97×C73—21no—
204C4×C8×C73—21no—
205C4×C8×C73—21no—
206C23×D73C22×C411yescharacteristic
207C2×Dic146—21no—
208C2×Dic146—21no—
209C2×Dic146—22no—
210C2×Dic146—41no—
211C2×C22⋊D73—21no—
212C2×C22⋊D73—21no—
213C2×C22⋊D73—42no—
214C22×Dic73—21no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73—21no—
218C22×Dic73—22no—
219C22×Dic73—41no—
220C22×Dic73—42no—
221C22×Dic73C22×C411yescharacteristic
222C22×Dic73C22×C411yescharacteristic
223C22×Dic73C22×C411yescharacteristic
224C22×Dic73C22×C411yescharacteristic
225C22×Dic73C22×C411yescharacteristic
226C22×Dic73C22×C411yescharacteristic
227C22×Dic73C22×C411yescharacteristic
228C2×C4×D73—21no—
229C2×C4×D73—21no—
230C2×C4×D73—22no—
231C2×C4×D73—41no—
232#11924012—42no—
233C2×#10596831—21no—
234C2×#10596831—21no—
235C2×#10596831—21no—
236C2×#10596831—21no—
237C2×#10596831—42no—
238C4⋊Dic73—21no—
239C4⋊Dic73—21no—
240C4⋊Dic73—21no—
241C4⋊Dic73—21no—
242C4⋊Dic73—21no—
243C4⋊Dic73—21no—
244#11924007—21no—
245#11924007—21no—
246#11924007—21no—
247#11924007—21no—
248#11924007—21no—
249#11924007—21no—
250#11924007—21no—
251#11924007—21no—
252#11924007—21no—
253#11924007—21no—
254#11924007—21no—
255#11924007—21no—
256#11924007—21no—
257#11924007—21no—
258#11924007—21no—
259#11924007—21no—
260#11924007—21no—
261#11924007—21no—
262#11924007—21no—
263#11924007—21no—
264#11924007—21no—
265#11924007—21no—
266C22⋊Dic73—21no—
267C22⋊Dic73—21no—
268#11924005—21no—
269#11924005—21no—
270#11924005—21no—
271#11924005—21no—
272#11924005—21no—
273#11924005—21no—
274#11924005—21no—
275#11924005—21no—
276#11924005—21no—
277#11924005—21no—
278C4×Dic73—21no—
279C4×Dic73—21no—
280C4×Dic73—21no—
281C4×Dic73—21no—
282C4×Dic73—21no—
283C4×Dic73—21no—
284C24×C73C22×C411yescharacteristic
285C22×C4×C73—42no—
286C22×C4×C73C22×C411yescharacteristic
287C22×C4×C73C22×C411yescharacteristic
288C22×C4×C73C22×C411yescharacteristic
289C22×C4×C73C22×C411yescharacteristic
290C22×C4×C73C22×C411yescharacteristic
291C22×C4×C73C2×D411yescharacteristic
292C22×C4×C73C2×D411yescharacteristic
293C22×C4×C73C2×D411yescharacteristic
294C22×C4×C73C2×D411yescharacteristic
295C22×C4×C73C2411yescharacteristic
296M16×C73—42no—
297C2×C8×C73—21no—
298C2×C8×C73—21no—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—42no—
302C4⋊C4×C73C22⋊C411yescharacteristic
303C4⋊C4×C73C22⋊C411yescharacteristic
304C4⋊C4×C73C22⋊C411yescharacteristic
305C4⋊C4×C73C22⋊C411yescharacteristic
306C4⋊C4×C73C22⋊C411yescharacteristic
307C4⋊C4×C73C22⋊C411yescharacteristic
308C4⋊C4×C73C22⋊C411yescharacteristic
309C4⋊C4×C73C22⋊C411yescharacteristic
310C22⋊C4×C73C22⋊C411yescharacteristic
311C22⋊C4×C73C22⋊C411yescharacteristic
312C22⋊C4×C73C22⋊C411yescharacteristic
313C22⋊C4×C73C22⋊C411yescharacteristic
314C22⋊C4×C73C22⋊C411yescharacteristic
315C22⋊C4×C73C22⋊C411yescharacteristic
316C22⋊C4×C73C22⋊C411yescharacteristic
317C22⋊C4×C73C22⋊C411yescharacteristic
318C42×C73C2×D411yescharacteristic
319C42×C73C2×D411yescharacteristic
320C42×C73C2×D411yescharacteristic
321C42×C73C2×D411yescharacteristic
322C42×C73C2×D411yescharacteristic
323C42×C73C2×D411yescharacteristic
324C42×C73C2×D411yescharacteristic
325C42×C73C2×D411yescharacteristic
326C23×C73—21no—
327C23×C73—21no—
328C23×C73—22no—
329C23×C73—41no—
330C23×C73C2×C22⋊C411yescharacteristic
331C23×C73C2×C22⋊C411yescharacteristic
332C23×C73C23×C411yescharacteristic
333C22×D73—21no—
334C22×D73—21no—
335C22×D73—21no—
336C22×D73—41no—
337C22×D73—41no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73C2×C22⋊C411yescharacteristic
351C2×C4×C73C2×C22⋊C411yescharacteristic
352C2×C4×C73C2×C22⋊C411yescharacteristic
353C2×C4×C73C2×C22⋊C411yescharacteristic
354C2×C4×C73C2×C22⋊C411yescharacteristic
355C2×C4×C73C2×C22⋊C411yescharacteristic
356C2×C4×C73C2×C22⋊C411yescharacteristic
357C2×C4×C73C2×C22⋊C411yescharacteristic
358C2×C4×C73C2×C22⋊C411yescharacteristic
359C2×C4×C73C2×C22⋊C411yescharacteristic
360C2×C4×C73C22×D411yescharacteristic
361C2×C4×C73C22×D411yescharacteristic
362C22⋊D73—42no—
363C22⋊D73—42no—
364C2×Dic73—21no—
365C2×Dic73—21no—
366C2×Dic73—21no—
367C2×Dic73—21no—
368C2×Dic73—21no—
369C2×Dic73—21no—
370C2×Dic73—21no—
371C2×Dic73—21no—
372C2×Dic73—21no—
373C2×Dic73—21no—
374C2×Dic73—21no—
375C2×Dic73—21no—
376C2×Dic73—42no—
377C2×Dic73—42no—
378C2×Dic73—42no—
379C2×Dic73—42no—
380C2×Dic73—41no—
381C2×Dic73—41no—
382C2×Dic73—41no—
383C2×Dic73—41no—
384C2×Dic73#13112yes—
385C4×D73—42no—
386C4×D73—42no—
387Dic146—42no—
388Dic146—42no—
389C8×C73—41no—
390C8×C73—41no—
391C8×C73—41no—
392C8×C73—41no—
393#10596831—41no—
394#10596831—41no—
395#10596831—41no—
396#10596831—41no—
397C22×C73—21no—
398C22×C73—21no—
399C22×C73—21no—
400C22×C73—21no—
401C22×C73—21no—
402C22×C73—21no—
403C22×C73—21no—
404C22×C73—42no—
405C22×C73—42no—
406C22×C73#41012yes—
407C22×C73C22×C22⋊C411yescharacteristic
408C22×C73C2×#13111yescharacteristic
409C22×C73#56811yescharacteristic
410C2×D73—41no—
411C2×D73—41no—
412C2×D73—41no—
413C2×D73—81no—
414C2×D73—81no—
415C4×C73—21no—
416C4×C73—21no—
417C4×C73—21no—
418C4×C73—21no—
419C4×C73—21no—
420C4×C73—21no—
421C4×C73—21no—
422C4×C73—21no—
423C4×C73—21no—
424C4×C73—21no—
425C4×C73—21no—
426C4×C73—21no—
427Dic73—22no—
428Dic73—41no—
429Dic73—41no—
430Dic73—41no—
431Dic73—41no—
432Dic73—41no—
433Dic73—41no—
434#17417—731nomaximal, Sylow
435C2×C73—21no—
436C2×C73—21no—
437C2×C73—22no—
438C2×C73—41no—
439C2×C73#288011yescharacteristic
440C2×C73C2×#41011yescharacteristic
441C2×C73#288911yescharacteristic
442D73—81no—
443C2×#552—731no—
444#2924—731no—
445#2924D7311yescharacteristic, complemented
446#1473—731no—
447#1473—731no—
448#1470—731no—
449#1470—731no—
450#1468—731no—
451#1468—731no—
452#1467—731no—
453#1464—731no—
454#1463—731no—
455#1461—731no—
456#1458—731no—
457C2×#324—731no—
458C73#1741711yescharacteristic, complemented, Sylow
459#552—1461no—
460#552—1461no—
461#552—1461no—
462#552—1461no—
463#552—1461no—
464#552—1461no—
465#552—1461no—
466#552—1461no—
467C2×#126—731no—
468C2×#126—731no—
469C2×#125—731no—
470C2×#125—731no—
471C2×#125—731no—
472C2×#123—731no—
473C2×#123—731no—
474C2×C22⋊Q8—731no—
475C2×C22⋊Q8—731no—
476C2×C4×Q8—731no—
477C2×C4×D4—731no—
478C2×#117—731no—
479C2×#117—731no—
480C2×#117C2×D7311yescharacteristic
481C22×C4⋊C4—731no—
482#433—21no—
483#433—21no—
484#433—1461no—
485#433—1461no—
486#432—731no—
487#432—731no—
488#432C2×D7311yescharacteristic
489#432C2×D7311yescharacteristic
490#431—731no—
491#431—731no—
492#431C2×D7311yescharacteristic
493#431C2×D7311yescharacteristic
494#424—21no—
495#424—1461no—
496#407—731no—
497#407C2×D7311yescharacteristic
498C2×C22⋊C8—731no—
499C2×C22⋊C8C2×D7311yescharacteristic
500#405—21no—
501#405—1461no—
502#324—731no—
503#324—731no—
504#324—731no—
505#324—731no—
506#324—731no—
507#324—731no—
508#324—731no—
509#324—731no—
510#324—731no—
511#324—731no—
512#324—731no—
513#324—731no—
514#323—731no—
515#323—731no—
516#323—731no—
517#323—731no—
518C22×Q8—731no—
519C22×D4—731no—
520C23×C4—731no—
521C23×C4—731no—
522C23×C4—731no—
523C23×C4C22×D7311yescharacteristic
524C2×M16—21no—
525C2×M16—1461no—
526C22×C8—21no—
527C22×C8—1461no—
528#126—1461no—
529#126—1461no—
530#126—1461no—
531#126—1461no—
532#126—1461no—
533#126—1461no—
534#126—1461no—
535#126—1461no—
536#125—1461no—
537#125—1461no—
538#125—1461no—
539#125—1461no—
540#125—1461no—
541#125—1461no—
542#125—1461no—
543#125—1461no—
544#125—1461no—
545#125—1461no—
546#125—1461no—
547#125—1461no—
548#123—1461no—
549#123—1461no—
550#123—1461no—
551#123—1461no—
552#123—1461no—
553#123—1461no—
554#123—1461no—
555#123—1461no—
556C22⋊Q8—1461no—
557C22⋊Q8—1461no—
558C22⋊Q8—1461no—
559C22⋊Q8—1461no—
560C22⋊Q8—1461no—
561C22⋊Q8—1461no—
562C22⋊Q8—1461no—
563C22⋊Q8—1461no—
564C4×Q8—1461no—
565C4×Q8—1461no—
566C4×Q8—1461no—
567C4×Q8—1461no—
568C4×D4—1461no—
569C4×D4—1461no—
570C4×D4—1461no—
571C4×D4—1461no—
572#117—1461no—
573#117—1461no—
574#117—1461no—
575#117—1461no—
576#117—1461no—
577#117—1461no—
578#117—1461no—
579#117—1461no—
580#117D29211yescharacteristic
581#117D29211yescharacteristic
582#117D29211yescharacteristic
583#117D29211yescharacteristic
584#117C22⋊D7311yescharacteristic
585#117C22⋊D7311yescharacteristic
586#117C22⋊D7311yescharacteristic
587#117C22⋊D7311yescharacteristic
588C2×C4⋊C4—731no—
589C2×C4⋊C4—731no—
590C2×C4⋊C4—731no—
591C2×C4⋊C4—731no—
592C2×C4⋊C4—731no—
593C2×C4⋊C4—731no—
594C2×C4⋊C4—731no—
595C2×C4⋊C4—731no—
596C2×C4⋊C4—731no—
597C2×C4⋊C4—731no—
598C2×C4⋊C4—731no—
599C2×C4⋊C4—731no—
600C2×C4⋊C4—731no—
601C2×C4⋊C4—731no—
602C2×C4⋊C4—1461no—
603C2×C4⋊C4—1461no—
604C2×C4⋊C4—1461no—
605C2×C4⋊C4—1461no—
606C2×C4⋊C4C4×D7311yescharacteristic
607C2×C4⋊C4C4×D7311yescharacteristic
608C2×C22⋊C4—731no—
609C2×C22⋊C4—731no—
610C2×C22⋊C4—731no—
611C2×C22⋊C4—731no—
612C2×C22⋊C4—731no—
613C2×C22⋊C4—731no—
614C2×C22⋊C4C4×D7311yescharacteristic
615C2×C22⋊C4C4×D7311yescharacteristic
616C2×C42—731no—
617C2×C42—731no—
618C2×C42—731no—
619C2×C42C22×D7311yescharacteristic
620C2×C42C22×D7311yescharacteristic
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625C4⋊C8—1461no—
626C4⋊C8—1461no—
627C4⋊C8—1461no—
628C4⋊C8—1461no—
629C22⋊C8—21no—
630C22⋊C8—21no—
631C22⋊C8—731no—
632C22⋊C8—731no—
633C22⋊C8—731no—
634C22⋊C8—731no—
635C22⋊C8—1461no—
636C22⋊C8—1461no—
637C22⋊C8C22×D7311yescharacteristic
638C22⋊C8C22×D7311yescharacteristic
639C22⋊C8C22×D7311yescharacteristic
640C22⋊C8C22×D7311yescharacteristic
641#97—21no—
642#97—21no—
643#97—1461no—
644#97—1461no—
645C4×C8—21no—
646C4×C8—21no—
647C4×C8—1461no—
648C4×C8—1461no—
649C24—731no—
650C24C2×C4×D7311yescharacteristic
651C2×Q8—2921no—
652C2×Q8—1462no—
653C2×Q8—1461no—
654C2×Q8—1461no—
655C2×D4—2922no—
656C2×D4—1461no—
657C2×D4—1461no—
658C22×C4—42no—
659C22×C4—2921no—
660C22×C4—2922no—
661C22×C4—2921no—
662C22×C4—731no—
663C22×C4—731no—
664C22×C4—731no—
665C22×C4—731no—
666C22×C4—731no—
667C22×C4—731no—
668C22×C4—731no—
669C22×C4—1462no—
670C22×C4—1462no—
671C22×C4—1461no—
672C22×C4—1461no—
673C22×C4—1461no—
674C22×C4—1461no—
675C22×C4—1461no—
676C22×C4—1461no—
677C22×C4C2×C4×D7311yescharacteristic
678C22×C4C2×C4×D7311yescharacteristic
679C22×C4C2×C4×D7311yescharacteristic
680C22×C4C2×C4×D7311yescharacteristic
681C22×C4C2×C4×D7311yescharacteristic
682C22×C4C2×C22⋊D7311yescharacteristic
683C22×C4C2×C22⋊D7311yescharacteristic
684C22×C4C2×D29211yescharacteristic
685C22×C4C2×D29211yescharacteristic
686C22×C4C23×D7311yescharacteristic
687M16—42no—
688M16—2922no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—2922no—
695C2×C8—1461no—
696C2×C8—1461no—
697C2×C8—1461no—
698C2×C8—1461no—
699C4⋊C4—1461no—
700C4⋊C4—1461no—
701C4⋊C4—1461no—
702C4⋊C4—1461no—
703C4⋊C4—1461no—
704C4⋊C4—1461no—
705C4⋊C4—1461no—
706C4⋊C4—1461no—
707C4⋊C4—1461no—
708C4⋊C4—1461no—
709C4⋊C4—1461no—
710C4⋊C4—1461no—
711C4⋊C4—1461no—
712C4⋊C4—1461no—
713C4⋊C4—1461no—
714C4⋊C4—1461no—
715C4⋊C4—1461no—
716C4⋊C4—1461no—
717C4⋊C4—1461no—
718C4⋊C4—1461no—
719C4⋊C4—1461no—
720C4⋊C4—1461no—
721C4⋊C4—1461no—
722C4⋊C4—1461no—
723C4⋊C4—1461no—
724C4⋊C4—1461no—
725C4⋊C4—1461no—
726C4⋊C4—1461no—
727C4⋊C4#1192400511yescharacteristic
728C4⋊C4#1192400511yescharacteristic
729C4⋊C4#1192400511yescharacteristic
730C4⋊C4#1192400511yescharacteristic
731C4⋊C4#1192400511yescharacteristic
732C4⋊C4#1192400511yescharacteristic
733C4⋊C4#1192400511yescharacteristic
734C4⋊C4#1192400511yescharacteristic
735C22⋊C4—1461no—
736C22⋊C4—1461no—
737C22⋊C4—1461no—
738C22⋊C4—1461no—
739C22⋊C4—1461no—
740C22⋊C4—1461no—
741C22⋊C4—1461no—
742C22⋊C4—1461no—
743C22⋊C4—1461no—
744C22⋊C4—1461no—
745C22⋊C4—1461no—
746C22⋊C4—1461no—
747C22⋊C4#1192400511yescharacteristic
748C22⋊C4#1192400511yescharacteristic
749C22⋊C4#1192400511yescharacteristic
750C22⋊C4#1192400511yescharacteristic
751C22⋊C4#1192400511yescharacteristic
752C22⋊C4#1192400511yescharacteristic
753C22⋊C4#1192400511yescharacteristic
754C22⋊C4#1192400511yescharacteristic
755C42—1461no—
756C42—1461no—
757C42—1461no—
758C42—1461no—
759C42—1461no—
760C42—1461no—
761C42C2×C22⋊D7311yescharacteristic
762C42C2×C22⋊D7311yescharacteristic
763C42C2×C22⋊D7311yescharacteristic
764C42C2×C22⋊D7311yescharacteristic
765C42C2×D29211yescharacteristic
766C42C2×D29211yescharacteristic
767C42C2×D29211yescharacteristic
768C42C2×D29211yescharacteristic
769C23—22no—
770C23—21no—
771C23—21no—
772C23—41no—
773C23—2921no—
774C23—2921no—
775C23—1461no—
776C23—1461no—
777C23—1461no—
778C23C2×#1192400511yescharacteristic
779C23C2×#1192400511yescharacteristic
780C23C22×C4×D7311yescharacteristic
781Q8—2922no—
782Q8—2922no—
783D4—2922no—
784D4—2922no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—2922no—
798C2×C4—2922no—
799C2×C4—2922no—
800C2×C4—2922no—
801C2×C4—2922no—
802C2×C4—2922no—
803C2×C4—2921no—
804C2×C4—2921no—
805C2×C4—2921no—
806C2×C4—2921no—
807C2×C4—732no—
808C2×C4—1461no—
809C2×C4—1461no—
810C2×C4—1461no—
811C2×C4—1461no—
812C2×C4—1461no—
813C2×C4—1461no—
814C2×C4—1461no—
815C2×C4—1461no—
816C2×C4—1461no—
817C2×C4—1461no—
818C2×C4—1461no—
819C2×C4—1461no—
820C2×C4C2×#1192400511yescharacteristic
821C2×C4C2×#1192400511yescharacteristic
822C2×C4C2×#1192400511yescharacteristic
823C2×C4C2×#1192400511yescharacteristic
824C2×C4C2×#1192400511yescharacteristic
825C2×C4C2×#1192400511yescharacteristic
826C2×C4C2×#1192400511yescharacteristic
827C2×C4C2×#1192400511yescharacteristic
828C2×C4C2×#1192400511yescharacteristic
829C2×C4C2×#1192400511yescharacteristic
830C2×C4C22×C22⋊D7311yescharacteristic
831C2×C4C22×D29211yescharacteristic
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—2921no—
837C8—2921no—
838C8—2921no—
839C8—2921no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—42no—
848C22—42no—
849C22—2921no—
850C22—2921no—
851C22—2921no—
852C22—5841no—
853C22—5841no—
854C22#1798856012yes—
855C22C22×#1192400511yescharacteristic
856C22#131×D7311yescharacteristic
857C22#1798935211yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—2921no—
871C4—2921no—
872C4—2921no—
873C4—2921no—
874C4—2921no—
875C4—2921no—
876C4—1462no—
877C2—21no—
878C2—21no—
879C2—22no—
880C2—41no—
881C2—5841no—
882C2#2261837811yescharacteristic
883C2C2×#1798856011yescharacteristic
884C2#2261841311yescharacteristic
subgroupG/H
centerC22C22×#11924005
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2924C2
socleC22×C73C22×C22⋊C4
prime radicalC22×C22⋊D73C2×C4
cosocleC22×C4×C73C24
hypercenter#2924D73
hypocenterC73#17417
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #22618589C2semidirect
3. #22608301C2semidirect
4. #22608298C2semidirect
5. #22608288C2semidirect
6. #22608286C2semidirect
9. #22608274C2semidirect
10. #22608263C2semidirect
11. #22608260C2semidirect
12. #22608254C2semidirect
13. #22608243C2semidirect
14. C2×#17988312C2semidirect
15. C73×#2924C2semidirect
445. #2924D73semidirect
458. C73#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#179892702
#226185892
#226083012
#226082982
#226082882
#226082862
#226082802
#226082772
#226082742
#226082632
#226082602
#226082542
#226082432
C2×#179883122
C73×#29242
#1741773