Finite Group Databasebeta

← #13526991

Subgroups — #13526991

Order 1792.

1766 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2618C211yesmaximal, characteristic
2#11740335C212yesmaximal, complemented
3#11740281C212yesmaximal, complemented
4#11740124C211yesmaximal, characteristic
5Dic7×#121C211yesmaximal, characteristic
6#11739628C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
8#11735244C212yesmaximal, complemented
9#11735222C212yesmaximal, complemented
10#11734767C212yesmaximal, complemented
11#11734766C212yesmaximal, complemented
12#11734756C212yesmaximal, complemented
13#11734743C212yesmaximal, complemented
14#11734404C212yesmaximal, complemented
15#11734367C212yesmaximal, complemented
16#11732315C212yesmaximal, complemented
17#11732108C212yesmaximal, complemented
18#11731401C211yesmaximal, characteristic, complemented
19#11731311C211yesmaximal, characteristic, complemented
20C2×C7×#123C2212yes—
21C2×C7×#121C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C2×D4×Dic7C2212yes—
24C2×D4×Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C2×#6487C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C2×#6450C2211yescharacteristic
31C2×#6442C2212yes—
32C7×#398C2212yes—
33C7×#396C2212yes—
34C7×#396C2212yes—
35C7×#394C2212yes—
36C7×#386C2212yes—
37C7×#380C2211yescharacteristic
38#89994C2212yes—
39#89993C2211yescharacteristic
40#89992C2212yes—
41#89992C2212yes—
42#89992C2212yes—
43#89984C2211yescharacteristic
44#89983C2212yes—
45#89982C2212yes—
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48#89758C2212yes—
49#89758C2212yes—
50#89757C2212yes—
51#89757C2212yes—
52#89757C2211yescharacteristic
53#89756C2212yes—
54#89756C2212yes—
55#89756C2212yes—
56#89754C2212yes—
57#89753C2212yes—
58#89753C2212yes—
59#89751C2212yes—
60#89750C2212yes—
61#89750C2212yes—
62#89750C2212yes—
63#89750C2212yes—
64C4⋊C4×Dic7C2212yes—
65C4⋊C4×Dic7C2211yescharacteristic
66C4⋊C4×Dic7C2212yes—
67C4⋊C4×Dic7C2211yescharacteristic
68C4⋊C4×Dic7C2212yes—
69C4⋊C4×Dic7C2212yes—
70#89746C2211yescharacteristic
71#89745C2211yescharacteristic
72#89725C2212yes—
73#89723C2212yes—
74#89723C2212yes—
75#89723C2212yes—
76#89723C2212yes—
77#89722C2212yes—
78#89722C2212yes—
79#89722C2212yes—
80#89719C2212yes—
81#89718C2212yes—
82#89718C2212yes—
83#89717C2212yes—
84#89717C2212yes—
85#89716C2212yes—
86#89716C2212yes—
87#89716C2212yes—
88#89716C2212yes—
89#89716C2212yes—
90#89716C2212yes—
91#89715C2212yes—
92#89714C2212yes—
93C22⋊C4×Dic7C2212yes—
94C22⋊C4×Dic7C2212yes—
95#89433C2212yes—
96#89432C2212yes—
97#89427C2212yes—
98#89426C2212yes—
99#89425C2212yes—
100#89425C2212yes—
101#89424C2212yes—
102#89424C2212yes—
103#89423C2212yes—
104#89423C2212yes—
105#89422C2212yes—
106#89421C2212yes—
107#35021—71nomaximal, Sylow
108C22×C7×D4C2312yes—
109C22×C7×D4C2311yescharacteristic
110C23×C4×C7C2311yescharacteristic
111C23×C4×C7C2311yescharacteristic
112C23×C4×C7C2311yescharacteristic
113C23×Dic7C2311yescharacteristic
114C23×Dic7C2311yescharacteristic
115C23×Dic7C2311yescharacteristic
116C23×Dic7C2312yes—
117C23×Dic7C2311yescharacteristic
118C22×Dic14C2311yescharacteristic
119C7×#123—28no—
120C7×#121—24no—
121C2×C7×C4⋊C4—24no—
122C2×C7×C4⋊C4C2312yes—
123C2×C7×C4⋊C4C2312yes—
124C2×C7×C4⋊C4C2311yescharacteristic
125C2×C7×C4⋊C4C2312yes—
126C2×C7×C4⋊C4C2312yes—
127C2×C7×C4⋊C4C2311yescharacteristic
128C2×C7×C4⋊C4C2311yescharacteristic
129C2×C7×C22⋊C4C2312yes—
130C2×C7×C22⋊C4C2312yes—
131C2×C7×C22⋊C4C2312yes—
132C2×C7×C22⋊C4C2312yes—
133C2×C7×C22⋊C4C2312yes—
134C2×C7×C22⋊C4C2312yes—
135C2×C22⋊Dic7C2312yes—
136C2×C22⋊Dic7C2312yes—
137C2×C22⋊Dic7C2312yes—
138C2×C22⋊Dic7C2312yes—
139C2×C22⋊Dic7C2312yes—
140C2×C22⋊Dic7C2312yes—
141C2×C22⋊Dic7C2312yes—
142C2×C22⋊Dic7C2312yes—
143C2×C22⋊Dic7C2312yes—
144D4×Dic7—28no—
145D4×Dic7—42no—
146C2×C4⋊Dic7—24no—
147C2×C4⋊Dic7C2312yes—
148C2×C4⋊Dic7C2311yescharacteristic
149C2×C4⋊Dic7C2312yes—
150C2×C4⋊Dic7C2312yes—
151C2×C4⋊Dic7C2312yes—
152C2×C4⋊Dic7C2312yes—
153C2×C4⋊Dic7C2311yescharacteristic
154C2×C4⋊Dic7C2311yescharacteristic
155#6487—24no—
156C2×Dic7⋊C4C2312yes—
157C2×Dic7⋊C4C2312yes—
158C2×Dic7⋊C4C2312yes—
159C2×Dic7⋊C4C2312yes—
160C2×Dic7⋊C4C2312yes—
161C2×Dic7⋊C4C2312yes—
162C2×Dic7⋊C4C2312yes—
163C2×C4×Dic7—24no—
164C2×C4×Dic7—42no—
165C2×C4×Dic7—42no—
166C2×C4×Dic7C2312yes—
167C2×C4×Dic7C2311yescharacteristic
168C2×C4×Dic7C2312yes—
169C2×C4×Dic7C2311yescharacteristic
170C2×C4×Dic7C2312yes—
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2312yes—
173C2×C4×Dic7C2311yescharacteristic
174C2×C4×Dic7C2312yes—
175C2×C4×Dic7C2312yes—
176C2×C4×Dic7C2311yescharacteristic
177#6450—42no—
178#6442—44no—
179C7×#95C2312yes—
180C7×#95C2312yes—
181C7×#95C2312yes—
182C7⋊#95C2312yes—
183C7⋊#95C2312yes—
184C7⋊#95C2312yes—
185C7⋊#95C2312yes—
186C7⋊#95C2312yes—
187C7⋊#95C2312yes—
188C7⋊#95C2312yes—
189C7⋊#95C2312yes—
190C7⋊#95C2312yes—
191C7⋊#95C2312yes—
192C7⋊#95C2312yes—
193C7⋊#95C2312yes—
194C7⋊#95C2312yes—
195C7⋊#95C2312yes—
196C7⋊#95C2312yes—
197C7⋊#95C2312yes—
198C7⋊#95C2312yes—
199C7⋊#95C2312yes—
200C7⋊#95C2312yes—
201C7⋊#95C2312yes—
202C7⋊#95C2312yes—
203C7⋊#95C2312yes—
204C7⋊#95C2312yes—
205C7⋊#95C2312yes—
206C7⋊#95C2312yes—
207#2853—72no—
208#2852—72no—
209#2646—71no—
210#2639—71no—
211#2627—71no—
212#2618D711yescharacteristic
213#2593—72no—
214#2585—72no—
215#2574—72no—
216#2573—72no—
217#2525—72no—
218#2524—72no—
219#2469—72no—
220#2468—72no—
221#2322—72no—
222#2318—72no—
223C4×C22⋊Q8—71no—
224C4×#121—71no—
225C2×C4×C4⋊C4—71no—
226C24×C7C2412yes—
227C24×C7C2411yescharacteristic
228C2×C7×D4—24no—
229C2×C7×D4—24no—
230C2×C7×D4—24no—
231C2×C7×D4—22no—
232C2×C7×D4—41no—
233C2×C7×D4—41no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—41no—
238C22×C4×C7—41no—
239C22×C4×C7—41no—
240C22×C4×C7—41no—
241C22×C4×C7#4114yes—
242C22×C4×C7#4114yes—
243C22×C4×C7C2412yes—
244C22×C4×C7C2412yes—
245C22×C4×C7C2412yes—
246C22×C4×C7C2412yes—
247C22×C4×C7C2412yes—
248C22×C4×C7C2411yescharacteristic
249C22×C4×C7C2411yescharacteristic
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—24no—
256C22×Dic7—41no—
257C22×Dic7—41no—
258C22×Dic7—41no—
259C22×Dic7—41no—
260C22×Dic7—41no—
261C22×Dic7—41no—
262C22×Dic7—42no—
263C22×Dic7—42no—
264C22×Dic7#4114yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2411yescharacteristic
272C22×Dic7C2411yescharacteristic
273C22×Dic7C2411yescharacteristic
274C22×Dic7C2411yescharacteristic
275C2×Dic14—22no—
276C2×Dic14—41no—
277C2×Dic14—41no—
278C7×C4⋊C4—24no—
279C7×C4⋊C4—24no—
280C7×C4⋊C4—22no—
281C7×C4⋊C4—24no—
282C7×C4⋊C4—24no—
283C7×C4⋊C4—41no—
284C7×C4⋊C4—41no—
285C7×C22⋊C4—24no—
286C7×C22⋊C4—24no—
287C7×C22⋊C4—24no—
288C7×C22⋊C4—24no—
289C7×C22⋊C4—42no—
290C7×C22⋊C4—42no—
291C22⋊Dic7—24no—
292C22⋊Dic7—24no—
293C22⋊Dic7—24no—
294C22⋊Dic7—24no—
295C22⋊Dic7—24no—
296C22⋊Dic7—42no—
297C22⋊Dic7—42no—
298C22⋊Dic7—42no—
299C22⋊Dic7—42no—
300C4⋊Dic7—22no—
301C4⋊Dic7—24no—
302C4⋊Dic7—24no—
303C4⋊Dic7—24no—
304C4⋊Dic7—42no—
305C4⋊Dic7—41no—
306C4⋊Dic7—42no—
307C4⋊Dic7—41no—
308Dic7⋊C4—24no—
309Dic7⋊C4—24no—
310Dic7⋊C4—24no—
311Dic7⋊C4—42no—
312Dic7⋊C4—42no—
313Dic7⋊C4—42no—
314Dic7⋊C4—42no—
315C4×Dic7—24no—
316C4×Dic7—24no—
317C4×Dic7—24no—
318C4×Dic7—24no—
319C4×Dic7—22no—
320C4×Dic7—22no—
321C4×Dic7—42no—
322C4×Dic7—41no—
323C4×Dic7—41no—
324C4×Dic7—42no—
325C4×Dic7—42no—
326C2×#126—72no—
327C2×#123C2×D712yes—
328C2×C22⋊Q8—71no—
329C2×#121C2×D711yescharacteristic
330C2×C4×Q8—71no—
331C2×C4×D4—72no—
332C2×C4×D4—71no—
333C22×C4⋊C4—71no—
334C22×C4⋊C4C2×D711yescharacteristic
335C22×C42—71no—
336C22×C42—71no—
337C22×C42—71no—
338#400—72no—
339#400—72no—
340#400—72no—
341#400—72no—
342#398—72no—
343#398—72no—
344#398—72no—
345#398—72no—
346#398C2×D712yes—
347#397—72no—
348#396C2×D712yes—
349#396C2×D712yes—
350#395—72no—
351#394—72no—
352#394C2×D712yes—
353#393—72no—
354#391—71no—
355#390—71no—
356#389—71no—
357#389—72no—
358#389—72no—
359#389—71no—
360#388—72no—
361#388—72no—
362#388—72no—
363#388—72no—
364#388—72no—
365#388—72no—
366#388—72no—
367#388—72no—
368#388—72no—
369#388—72no—
370#388—72no—
371#388—72no—
372#387—72no—
373#387—72no—
374#387—72no—
375#387—72no—
376#387—72no—
377#387—72no—
378#387—72no—
379#387—72no—
380#387—72no—
381#387—72no—
382#387—72no—
383#387—72no—
384#386—72no—
385#386—72no—
386#386—72no—
387#386C2×D712yes—
388#385—72no—
389#385—72no—
390#385—72no—
391#385—72no—
392#385—72no—
393#385—72no—
394#383—72no—
395#383—72no—
396#382—72no—
397#381—72no—
398#381—72no—
399#380—71no—
400#380—72no—
401#380C2×D711yescharacteristic
402C4×C4⋊C4—72no—
403C4×C4⋊C4—72no—
404C4×C4⋊C4—72no—
405C4×C4⋊C4—72no—
406C4×C4⋊C4—71no—
407C4×C4⋊C4—71no—
408C4×C4⋊C4—72no—
409C4×C22⋊C4—72no—
410C4×C22⋊C4—72no—
411C2×#95—71no—
412C2×#95—71no—
413C23×C7—21no—
414C23×C7—21no—
415C23×C7—21no—
416C23×C7—21no—
417C23×C7—22no—
418C23×C7—22no—
419C23×C7—22no—
420C23×C7—22no—
421C23×C7—22no—
422C23×C7—22no—
423C23×C7—22no—
424C23×C7C2×#4112yes—
425C23×C7C2×#4112yes—
426C23×C7C2×#4112yes—
427C23×C7C2511yescharacteristic
428C7×D4—44no—
429C7×D4—48no—
430C2×C4×C7—28no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—21no—
434C2×C4×C7—21no—
435C2×C4×C7—21no—
436C2×C4×C7—21no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—44no—
450C2×C4×C7—44no—
451C2×C4×C7C2×#4114yes—
452C2×C4×C7C2×#4112yes—
453C2×C4×C7C2×#4112yes—
454C2×Dic7—28no—
455C2×Dic7—21no—
456C2×Dic7—21no—
457C2×Dic7—21no—
458C2×Dic7—21no—
459C2×Dic7—21no—
460C2×Dic7—21no—
461C2×Dic7—21no—
462C2×Dic7—21no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—44no—
482C2×Dic7—44no—
483C2×Dic7—44no—
484C2×Dic7—84no—
485C2×Dic7C2×#4112yes—
486C2×Dic7C2×#4112yes—
487C2×Dic7H(5,𝔽2)12yes—
488C2×Dic72−1+412yes—
489Dic14—44no—
490C22×Q8—71no—
491C22×D4C22×D712yes—
492C22×D4C22×D711yescharacteristic
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—71no—
496C23×C4—72no—
497C23×C4—71no—
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D711yescharacteristic
501#126—284no—
502#123—28no—
503C22⋊Q8—144no—
504#121—24no—
505C4×Q8—282no—
506C4×D4—148no—
507C4×D4—282no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—72no—
510C2×C4⋊C4—72no—
511C2×C4⋊C4—72no—
512C2×C4⋊C4—72no—
513C2×C4⋊C4—72no—
514C2×C4⋊C4—71no—
515C2×C4⋊C4—72no—
516C2×C4⋊C4—71no—
517C2×C4⋊C4—72no—
518C2×C4⋊C4—72no—
519C2×C4⋊C4—72no—
520C2×C4⋊C4—72no—
521C2×C4⋊C4—72no—
522C2×C4⋊C4—71no—
523C2×C4⋊C4—72no—
524C2×C4⋊C4—144no—
525C2×C4⋊C4C22×D712yes—
526C2×C4⋊C4C22×D712yes—
527C2×C4⋊C4C22×D711yescharacteristic
528C2×C4⋊C4C22×D712yes—
529C2×C4⋊C4C22×D712yes—
530C2×C4⋊C4C22×D711yescharacteristic
531C2×C4⋊C4C22×D711yescharacteristic
532C2×C22⋊C4—72no—
533C2×C22⋊C4—72no—
534C2×C22⋊C4—72no—
535C2×C22⋊C4—72no—
536C2×C22⋊C4—72no—
537C2×C22⋊C4—72no—
538C2×C22⋊C4—72no—
539C2×C22⋊C4—72no—
540C2×C22⋊C4—72no—
541C2×C22⋊C4C22×D712yes—
542C2×C22⋊C4C22×D712yes—
543C2×C22⋊C4C22×D712yes—
544C2×C22⋊C4C22×D712yes—
545C2×C22⋊C4C22×D712yes—
546C2×C22⋊C4C22×D712yes—
547C2×C42—72no—
548C2×C42—71no—
549C2×C42—71no—
550C2×C42—72no—
551C2×C42—72no—
552C2×C42—72no—
553C2×C42—72no—
554C2×C42—71no—
555C2×C42—72no—
556C2×C42—71no—
557C2×C42—72no—
558C2×C42—144no—
559C2×C42—282no—
560C2×C42—282no—
561#95—72no—
562#95—72no—
563#95—72no—
564#95—72no—
565#95—72no—
566#95—72no—
567#95—72no—
568#95—72no—
569#95—72no—
570#95—72no—
571#95—72no—
572#95—72no—
573#95—72no—
574#95—72no—
575#95—72no—
576#95—72no—
577#95—72no—
578#95—72no—
579#95—72no—
580#95—72no—
581#95—72no—
582#95—72no—
583#95—72no—
584#95—72no—
585#95—72no—
586#95C22×D712yes—
587#95C22×D712yes—
588#95C22×D712yes—
589C22×C7—22no—
590C22×C7—22no—
591C22×C7—22no—
592C22×C7—22no—
593C22×C7—22no—
594C22×C7—22no—
595C22×C7—42no—
596C22×C7—42no—
597C22×C7—42no—
598C22×C7—42no—
599C22×C7—42no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7#52914yes—
603C22×C7C22×#4111yescharacteristic
604C22×C7C22×#4111yescharacteristic
605C22×C7C22×#4111yescharacteristic
606C22×C7C2×H(5,𝔽2)11yescharacteristic
607C22×C7C2×2−1+411yescharacteristic
608C22×C7#58511yescharacteristic
609C22×C7#58511yescharacteristic
610C4×C7—24no—
611C4×C7—22no—
612C4×C7—22no—
613C4×C7—42no—
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—42no—
617Dic7—22no—
618Dic7—22no—
619Dic7—22no—
620Dic7—22no—
621Dic7—42no—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626Dic7—42no—
627C24C23×D712yes—
628C24C23×D711yescharacteristic
629C2×Q8—142no—
630C2×Q8—281no—
631C2×Q8—281no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—22no—
636C2×D4—41no—
637C2×D4—41no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—71no—
646C22×C4—71no—
647C22×C4—71no—
648C22×C4—71no—
649C22×C4—74no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—72no—
655C22×C4—72no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—144no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—281no—
663C22×C4—281no—
664C22×C4—281no—
665C22×C4—281no—
666C22×C4—281no—
667C22×C4—281no—
668C22×C4—282no—
669C22×C4—282no—
670C22×C4#115914yes—
671C22×C4#115914yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C22×C4C23×D711yescharacteristic
678C22×C4C23×D711yescharacteristic
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—144no—
687C4⋊C4—144no—
688C4⋊C4—144no—
689C4⋊C4—144no—
690C4⋊C4—144no—
691C4⋊C4—144no—
692C4⋊C4—142no—
693C4⋊C4—282no—
694C4⋊C4—282no—
695C4⋊C4—282no—
696C4⋊C4—282no—
697C4⋊C4—281no—
698C4⋊C4—282no—
699C4⋊C4—281no—
700C4⋊C4—282no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—144no—
708C22⋊C4—144no—
709C22⋊C4—144no—
710C22⋊C4—144no—
711C22⋊C4—144no—
712C22⋊C4—282no—
713C22⋊C4—282no—
714C22⋊C4—282no—
715C22⋊C4—282no—
716C42—142no—
717C42—142no—
718C42—144no—
719C42—144no—
720C42—144no—
721C42—144no—
722C42—282no—
723C42—281no—
724C42—281no—
725C42—282no—
726C42—282no—
727C2×C7—24no—
728C2×C7—82no—
729C2×C7C2×#52911yescharacteristic
730C2×C7#345911yescharacteristic
731C2×C7#346111yescharacteristic
732C2×C7#349211yescharacteristic
733C2×C7#349311yescharacteristic
734C2×C7#350511yescharacteristic
735C2×C7#350711yescharacteristic
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23C2×#115912yes—
748C23C2×#115912yes—
749C23D7×#4112yes—
750C23C24×D711yescharacteristic
751Q8—284no—
752D4—44no—
753D4—48no—
754C2×C4—28no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—72no—
776C2×C4—72no—
777C2×C4—72no—
778C2×C4—72no—
779C2×C4—148no—
780C2×C4—141no—
781C2×C4—141no—
782C2×C4—141no—
783C2×C4—141no—
784C2×C4—141no—
785C2×C4—141no—
786C2×C4—141no—
787C2×C4—141no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—284no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4—564no—
810C2×C4C2×#115914yes—
811C2×C4C2×#115912yes—
812C2×C4C2×#115912yes—
813C7#3502111yescharacteristic, complemented, Sylow
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22#9029114yes—
828C22C22×#115911yescharacteristic
829C22C22×#115911yescharacteristic
830C22C2×D7×#4111yescharacteristic
831C22D7×H(5,𝔽2)11yescharacteristic
832C22#9061811yescharacteristic
833C22D7×2−1+411yescharacteristic
834C22#9062011yescharacteristic
835C4—24no—
836C4—22no—
837C4—22no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—142no—
843C4—142no—
844C4—142no—
845C4—142no—
846C4—282no—
847C4—282no—
848C4—282no—
849C4—282no—
850C4—282no—
851C4—282no—
852C2—24no—
853C2—82no—
854C2C2×#9029111yescharacteristic
855C2#1174336311yescharacteristic
856C2#1174340711yescharacteristic
857C2#1174343411yescharacteristic
858C2#1174344911yescharacteristic
859C2#1174349911yescharacteristic
860C2#1174352211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2618C2
prime radicalC2×C7×#121C22
hypercenter#2618D7
hypocenterC7#35021
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2618

Complements

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

NH ≅ G/Ntype
2. #11740335C2semidirect
3. #11740281C2semidirect
6. #11739628C2semidirect
7. C2×C4⋊C4×Dic7C2semidirect
8. #11735244C2semidirect
9. #11735222C2semidirect
10. #11734767C2semidirect
11. #11734766C2semidirect
12. #11734756C2semidirect
13. #11734743C2semidirect
14. #11734404C2semidirect
15. #11734367C2semidirect
16. #11732315C2semidirect
17. #11732108C2semidirect
18. #11731401C2semidirect
19. #11731311C2semidirect
813. C7#35021semidirect

Maximal subgroups

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

subgroupindex
C7×#26182
#117403352
#117402812
#117401242
Dic7×#1212
#117396282
C2×C4⋊C4×Dic72
#117352442
#117352222
#117347672
#117347662
#117347562
#117347432
#117344042
#117343672
#117323152
#117321082
#117314012
#117313112
#350217