Finite Group Databasebeta

← #13526362

Subgroups — #13526362

Order 1792.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90344C211yesmaximal, characteristic
2C22×C4×D28C211yesmaximal, characteristic, complemented
3C7×#2853C211yesmaximal, characteristic, complemented
4#11740311C211yesmaximal, characteristic, complemented
5#11739524C211yesmaximal, characteristic, complemented
6#11733294C212yesmaximal, complemented
7#11733293C212yesmaximal, complemented
8#11733290C212yesmaximal, complemented
9#11733289C212yesmaximal, complemented
10#11732765C212yesmaximal, complemented
11#11732764C212yesmaximal, complemented
12#11732761C212yesmaximal, complemented
13#11732760C212yesmaximal, complemented
14#11732381C211yesmaximal, characteristic, complemented
15#11732351C211yesmaximal, characteristic, complemented
16#11732319C211yesmaximal, characteristic, complemented
17D7×#386C211yesmaximal, characteristic, complemented
18#11732101C211yesmaximal, characteristic, complemented
19#11732064C211yesmaximal, characteristic, complemented
20#11732036C211yesmaximal, characteristic, complemented
21D7×#385C211yesmaximal, characteristic, complemented
22#11731581C211yesmaximal, characteristic, complemented
23#11731564C211yesmaximal, characteristic, complemented
24C22×D4×D7C2211yescharacteristic
25C23×D28C2211yescharacteristic
26C23×C4×D7C2211yescharacteristic
27C23×C4×D7C2211yescharacteristic, complemented
28C2×C7×#123C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic, complemented
30C2×#6500C2211yescharacteristic
31C2×#6492C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic, complemented
34C22×C4⋊Dic7C2211yescharacteristic, complemented
35#90344—28no—
36C2×#6458C2211yescharacteristic
37C2×#6458C2211yescharacteristic
38C2×#6457C2211yescharacteristic
39C2×#6457C2211yescharacteristic
40C2×#6457C2212yescomplemented
41C2×D7×C4⋊C4C2212yescomplemented
42C2×#6447C2211yescharacteristic
43C2×#6447C2211yescharacteristic
44C2×#6446C2212yescomplemented
45C2×#6445C2211yescharacteristic
46C2×#6445C2211yescharacteristic
47C2×#6445C2211yescharacteristic
48C2×D7×C22⋊C4C2211yescharacteristic
49C2×D7×C22⋊C4C2211yescharacteristic
50C2×D7×C22⋊C4C2211yescharacteristic
51C2×D7×C22⋊C4C2212yescomplemented
52C2×C4×D28—28no—
53C2×C4×D28C2212yes—
54C2×C4×D28C2212yes—
55C2×C4×D28C2212yescomplemented
56C2×C4×D28C2212yescomplemented
57C7×#388C2212yescomplemented
58C7×#388C2212yescomplemented
59C7×#387C2212yescomplemented
60C7×#387C2212yescomplemented
61C7×#386C2211yescharacteristic
62C7×#386C2211yescharacteristic
63C7×#385C2211yescharacteristic, complemented
64C7×#385C2211yescharacteristic, complemented
65C7×#381C2211yescharacteristic, complemented
66#89992C2211yescharacteristic
67#89992C2211yescharacteristic
68#89985C2211yescharacteristic
69#89985C2211yescharacteristic
70#89983C2211yescharacteristic, complemented
71#89982C2211yescharacteristic, complemented
72#89982C2211yescharacteristic, complemented
73#89765C2212yescomplemented
74#89763C2212yescomplemented
75#89761C2212yescomplemented
76#89761C2212yescomplemented
77#89761C2212yescomplemented
78#89759C2212yescomplemented
79#89758C2212yescomplemented
80#89755C2212yescomplemented
81#89733C2212yescomplemented
82#89731C2212yescomplemented
83#89730C2211yescharacteristic
84#89730C2211yescharacteristic
85#89728C2212yescomplemented
86#89728C2212yescomplemented
87#89728C2212yescomplemented
88#89727C2212yescomplemented
89#89727C2211yescharacteristic, complemented
90#89727C2211yescharacteristic, complemented
91#89725C2212yescomplemented
92#89722C2211yescharacteristic, complemented
93#89722C2211yescharacteristic, complemented
94#89721C2212yescomplemented
95#89718C2211yescharacteristic, complemented
96#89718C2211yescharacteristic, complemented
97#89712C2212yescomplemented
98#89712C2212yescomplemented
99#89705C2212yescomplemented
100#89705C2212yescomplemented
101#89449C2212yescomplemented
102#89447C2212yescomplemented
103#89447C2212yescomplemented
104#89446C2212yescomplemented
105#89446C2212yescomplemented
106#89444C2212yescomplemented
107#89440C2212yescomplemented
108#89440C2212yescomplemented
109#89440C2212yescomplemented
110#89439C2212yescomplemented
111#89437C2212yes—
112#89437C2212yes—
113#89437C2212yescomplemented
114#89437C2212yescomplemented
115#89437C2212yescomplemented
116#89437C2212yescomplemented
117#89437C2212yescomplemented
118#89436C2212yescomplemented
119#89436C2212yescomplemented
120#89436C2212yescomplemented
121D7×#95C2212yescomplemented
122D7×#95C2212yescomplemented
123#89433C2212yescomplemented
124#89431C2212yescomplemented
125#34983—71nomaximal, Sylow
126C24×D7C2311yescharacteristic
127C24×D7C2311yescharacteristic
128C24×D7C2311yescharacteristic
129C22×C7×D4C2311yescharacteristic
130C23×C4×C7C2311yescharacteristic
131C23×C4×C7C2311yescharacteristic
132C23×C4×C7C2311yescharacteristic
133C22×C22⋊D7C2311yescharacteristic
134C22×C22⋊D7C2311yescharacteristic
135C22×C22⋊D7C2311yescharacteristic
136C22×C22⋊D7C2311yescharacteristic
137C23×Dic7C2311yescharacteristic
138C23×Dic7C2311yescharacteristic
139C2×D4×D7—24no—
140C2×D4×D7—24no—
141C2×D4×D7—24no—
142C22×D28—24no—
143C22×D28—24no—
144C22×D28D418yes—
145C22×D28C2311yescharacteristic
146C22×D28C2311yescharacteristic
147C22×D28C2311yescharacteristic
148C22×D28C2311yescharacteristic
149C22×D28C2311yescharacteristic
150C22×D28C2311yescharacteristic
151C22×D28C2311yescharacteristic
152C22×C4×D7—24no—
153C22×C4×D7—24no—
154C22×C4×D7—44no—
155C22×C4×D7—44no—
156C22×C4×D7C2311yescharacteristic
157C22×C4×D7C2312yes—
158C22×C4×D7C2312yes—
159C22×C4×D7C2312yes—
160C22×C4×D7C2312yes—
161C22×C4×D7C2312yes—
162C22×C4×D7C2311yescharacteristic
163C22×C4×D7C2311yescharacteristic
164C22×C4×D7C2312yes—
165C7×#123—24no—
166C2×C7×C4⋊C4C2312yes—
167C2×C7×C4⋊C4C2311yescharacteristic
168C2×C7×C4⋊C4C2311yescharacteristic
169C2×C7×C4⋊C4C2312yes—
170C2×C7×C22⋊C4C2311yescharacteristic
171C2×C7×C22⋊C4C2311yescharacteristic
172C2×C7×C22⋊C4C2311yescharacteristic
173C2×C7×C22⋊C4C2312yes—
174C2×C7×C22⋊C4C2311yescharacteristic
175C2×C7×C22⋊C4C2311yescharacteristic
176C2×C7×C22⋊C4C2312yes—
177C2×C42×C7—24no—
178C2×C42×C7C2312yes—
179C2×C42×C7C2312yes—
180C2×C22⋊Dic7C2311yescharacteristic
181C2×C22⋊Dic7C2311yescharacteristic
182C2×C22⋊Dic7C2311yescharacteristic
183C2×C22⋊Dic7C2312yes—
184C2×C22⋊Dic7C2312yes—
185#6500—24no—
186#6492—24no—
187C2×(C2×D7)⋊C4—24no—
188C2×(C2×D7)⋊C4—24no—
189C2×(C2×D7)⋊C4C2312yes—
190C2×(C2×D7)⋊C4C2312yes—
191C2×(C2×D7)⋊C4C2312yes—
192C2×(C2×D7)⋊C4C2312yes—
193C2×(C2×D7)⋊C4C2311yescharacteristic
194C2×(C2×D7)⋊C4C2311yescharacteristic
195C2×(C2×D7)⋊C4C2312yes—
196C2×(C2×D7)⋊C4C2312yes—
197C2×(C2×D7)⋊C4C2312yes—
198C2×(C2×D7)⋊C4C2311yescharacteristic
199C2×(C2×D7)⋊C4C2311yescharacteristic
200C2×(C2×D7)⋊C4C2311yescharacteristic
201C2×(C2×D7)⋊C4C2311yescharacteristic
202C2×(C2×D7)⋊C4C2311yescharacteristic
203C2×(C2×D7)⋊C4C2311yescharacteristic
204C2×(C2×D7)⋊C4C2312yes—
205C2×(C2×D7)⋊C4C2312yes—
206C2×(C2×D7)⋊C4C2312yes—
207C2×(C2×D7)⋊C4C2312yes—
208C2×(C2×D7)⋊C4C2312yes—
209C2×(C2×D7)⋊C4C2312yes—
210C2×(C2×D7)⋊C4C2312yes—
211C2×C4⋊Dic7—24no—
212C2×C4⋊Dic7C2312yes—
213C2×C4⋊Dic7C2312yes—
214C2×C4⋊Dic7C2312yes—
215C2×C4⋊Dic7C2312yes—
216C2×Dic7⋊C4C2312yes—
217C2×Dic7⋊C4C2311yescharacteristic
218C2×Dic7⋊C4C2311yescharacteristic
219C2×Dic7⋊C4C2312yes—
220C2×Dic7⋊C4C2312yes—
221C2×Dic7⋊C4C2312yes—
222#6458—24no—
223#6458—24no—
224#6457—24no—
225#6457—24no—
226#6457—44no—
227D7×C4⋊C4—44no—
228#6447—24no—
229#6447—24no—
230#6446—44no—
231#6445—24no—
232#6445—24no—
233#6445—24no—
234D7×C22⋊C4—24no—
235D7×C22⋊C4—24no—
236D7×C22⋊C4—24no—
237D7×C22⋊C4—44no—
238C4×D28—28no—
239C4×D28—28no—
240C4×D28—28no—
241C4×D28—28no—
242C7×#95C2312yes—
243C7×#95C2312yes—
244C7×#95C2312yes—
245C7×#95C2312yes—
246C7×#95C2312yes—
247C7×#95C2312yes—
248C7⋊#95C2312yes—
249C7⋊#95C2312yes—
250C7⋊#95C2312yes—
251C7⋊#95C2312yes—
252C7⋊#95C2312yes—
253C7⋊#95C2312yes—
254C7⋊#95C2312yes—
255C7⋊#95C2312yes—
256C7⋊#95C2312yes—
257C7⋊#95C2312yes—
258C7⋊#95C2312yes—
259C7⋊#95C2312yes—
260C7⋊#95C2312yes—
261C7⋊#95C2312yes—
262C2×#534—71no—
263C22×C4×D4—71no—
264#2853—71no—
265#2853D711yescharacteristic, complemented
266#2849—71no—
267#2849—71no—
268#2623—71no—
269#2623—71no—
270#2622—71no—
271#2622—71no—
272#2444—72no—
273#2444—72no—
274#2443—72no—
275#2443—72no—
276#2419—72no—
277#2419—72no—
278#2418—72no—
279#2418—72no—
280#2315—71no—
281#2308—71no—
282#2308—71no—
283C2×#386—71no—
284C2×#385—71no—
285C24×C7C2411yescharacteristic
286C24×C7C2411yescharacteristic
287C23×D7—22no—
288C23×D7—22no—
289C23×D7—22no—
290C23×D7—22no—
291C23×D7—22no—
292C23×D7—42no—
293C23×D7—42no—
294C23×D7—42no—
295C23×D7—42no—
296C23×D7—42no—
297C23×D7—42no—
298C23×D7C2×D414yes—
299C23×D7C2×D414yes—
300C23×D7#4114yes—
301C23×D7#4114yes—
302C23×D7C2411yescharacteristic
303C23×D7C2411yescharacteristic
304C23×D7C2411yescharacteristic
305C23×D7C2411yescharacteristic
306C23×D7C2411yescharacteristic
307C2×C7×D4—22no—
308C2×C7×D4—22no—
309C2×C7×D4—22no—
310C22×C4×C7—22no—
311C22×C4×C7—22no—
312C22×C4×C7—22no—
313C22×C4×C7—24no—
314C22×C4×C7—22no—
315C22×C4×C7—42no—
316C22×C4×C7C2×D414yes—
317C22×C4×C7C2411yescharacteristic
318C22×C4×C7C2411yescharacteristic
319C22×C4×C7C2412yes—
320C22×C4×C7C2412yes—
321C22×C4×C7C2412yes—
322C22×C4×C7C2411yescharacteristic
323C22×C4×C7C2411yescharacteristic
324C22×C4×C7C2411yescharacteristic
325C22×C4×C7C2412yes—
326C2×C22⋊D7—22no—
327C2×C22⋊D7—22no—
328C2×C22⋊D7—22no—
329C2×C22⋊D7—22no—
330C2×C22⋊D7—22no—
331C2×C22⋊D7—22no—
332C2×C22⋊D7—22no—
333C2×C22⋊D7—22no—
334C2×C22⋊D7—42no—
335C2×C22⋊D7—42no—
336C22×Dic7—22no—
337C22×Dic7—22no—
338C22×Dic7—42no—
339C22×Dic7—42no—
340C22×Dic7C2411yescharacteristic
341C22×Dic7C2411yescharacteristic
342C22×Dic7C2412yes—
343C22×Dic7C2412yes—
344C22×Dic7C2412yes—
345C22×Dic7C2412yes—
346C22×Dic7C2411yescharacteristic
347D4×D7—416no—
348C2×D28—232no—
349C2×D28—22no—
350C2×D28—22no—
351C2×D28—22no—
352C2×D28—22no—
353C2×D28—22no—
354C2×D28—22no—
355C2×D28—22no—
356C2×D28—22no—
357C2×D28—22no—
358C2×D28—22no—
359C2×D28—22no—
360C2×D28—22no—
361C2×D28—22no—
362C2×D28—42no—
363C2×D28—42no—
364C2×D28C2×D414yes—
365C2×D28C2×D414yes—
366C2×D28C2×D414yes—
367C2×D28C2×D414yes—
368C2×C4×D7—24no—
369C2×C4×D7—24no—
370C2×C4×D7—24no—
371C2×C4×D7—24no—
372C2×C4×D7—22no—
373C2×C4×D7—24no—
374C2×C4×D7—22no—
375C2×C4×D7—22no—
376C2×C4×D7—24no—
377C2×C4×D7—24no—
378C2×C4×D7—24no—
379C2×C4×D7—24no—
380C2×C4×D7—22no—
381C2×C4×D7—22no—
382C2×C4×D7—24no—
383C2×C4×D7—42no—
384C2×C4×D7—42no—
385C2×C4×D7—42no—
386C2×C4×D7—42no—
387C2×C4×D7—42no—
388C2×C4×D7—42no—
389C2×C4×D7—416no—
390C2×C4×D7—416no—
391C2×C4×D7—42no—
392C2×C4×D7—42no—
393C2×C4×D7—42no—
394C2×C4×D7—42no—
395C7×C4⋊C4—22no—
396C7×C4⋊C4—22no—
397C7×C4⋊C4—24no—
398C7×C4⋊C4—42no—
399C7×C22⋊C4—22no—
400C7×C22⋊C4—22no—
401C7×C22⋊C4—22no—
402C7×C22⋊C4—22no—
403C7×C22⋊C4—22no—
404C7×C22⋊C4—24no—
405C7×C22⋊C4—42no—
406C42×C7—24no—
407C42×C7—24no—
408C22⋊Dic7—22no—
409C22⋊Dic7—22no—
410C22⋊Dic7—22no—
411C22⋊Dic7—42no—
412C22⋊Dic7—42no—
413(C2×D7)⋊C4—24no—
414(C2×D7)⋊C4—24no—
415(C2×D7)⋊C4—24no—
416(C2×D7)⋊C4—24no—
417(C2×D7)⋊C4—22no—
418(C2×D7)⋊C4—22no—
419(C2×D7)⋊C4—22no—
420(C2×D7)⋊C4—22no—
421(C2×D7)⋊C4—22no—
422(C2×D7)⋊C4—22no—
423(C2×D7)⋊C4—24no—
424(C2×D7)⋊C4—24no—
425(C2×D7)⋊C4—22no—
426(C2×D7)⋊C4—22no—
427(C2×D7)⋊C4—24no—
428(C2×D7)⋊C4—42no—
429(C2×D7)⋊C4—42no—
430(C2×D7)⋊C4—42no—
431(C2×D7)⋊C4—42no—
432(C2×D7)⋊C4—42no—
433(C2×D7)⋊C4—42no—
434(C2×D7)⋊C4—42no—
435C4⋊Dic7—24no—
436C4⋊Dic7—24no—
437C4⋊Dic7—42no—
438C4⋊Dic7—42no—
439Dic7⋊C4—22no—
440Dic7⋊C4—22no—
441Dic7⋊C4—24no—
442Dic7⋊C4—42no—
443Dic7⋊C4—42no—
444Dic7⋊C4—42no—
445C23×D4—71no—
446C23×D4—71no—
447C24×C4—71no—
448C24×C4—71no—
449#534—148no—
450C2×#123—71no—
451C2×#123—71no—
452C2×#123—71no—
453C2×#123—72no—
454C2×#123—72no—
455C2×#123C2×D711yescharacteristic
456C2×#121—71no—
457C2×#121—71no—
458C2×#121—71no—
459C2×#121—71no—
460C2×#120—71no—
461C2×#120—71no—
462C2×#120—71no—
463C2×#120—71no—
464C2×C4×D4—72no—
465C2×C4×D4—72no—
466C2×C4×D4—72no—
467C2×C4×D4—72no—
468C2×C4×D4—148no—
469C22×C4⋊C4—71no—
470C22×C4⋊C4—72no—
471C22×C22⋊C4—71no—
472C22×C22⋊C4—71no—
473C22×C22⋊C4—71no—
474C22×C22⋊C4—71no—
475C22×C22⋊C4—71no—
476C22×C22⋊C4—72no—
477C22×C42C2×D711yescharacteristic, complemented
478#400—72no—
479#400—72no—
480#399—72no—
481#399—72no—
482#398—72no—
483#398—72no—
484#397—72no—
485#397—72no—
486#397—72no—
487#397—72no—
488#397—72no—
489#397—72no—
490#394—72no—
491#394—72no—
492#394—72no—
493#394—72no—
494#388—72no—
495#388—72no—
496#388C2×D712yescomplemented
497#388C2×D712yescomplemented
498#387—72no—
499#387—72no—
500#387C2×D712yescomplemented
501#387C2×D712yescomplemented
502#386—71no—
503#386—71no—
504#386—71no—
505#386—71no—
506#386—71no—
507#386—72no—
508#386—72no—
509#386—71no—
510#386—72no—
511#386—72no—
512#386—72no—
513#386—72no—
514#386—72no—
515#386—72no—
516#386—72no—
517#386—72no—
518#386C2×D711yescharacteristic
519#386C2×D711yescharacteristic
520#385—71no—
521#385—71no—
522#385—72no—
523#385—72no—
524#385—72no—
525#385—71no—
526#385—71no—
527#385—71no—
528#385—71no—
529#385—72no—
530#385—72no—
531#385—72no—
532#385C2×D711yescharacteristic, complemented
533#385C2×D711yescharacteristic, complemented
534#381—71no—
535#381—72no—
536#381—72no—
537#381—72no—
538#381C2×D711yescharacteristic, complemented
539#380—72no—
540#380—72no—
541#379—71no—
542#379—71no—
543#379—72no—
544C2×#95—72no—
545C2×#95—72no—
546C23×C7—22no—
547C23×C7—22no—
548C23×C7—21no—
549C23×C7—21no—
550C23×C7—21no—
551C23×C7—22no—
552C23×C7—22no—
553C23×C7C22×D412yes—
554C23×C7C2×#4112yes—
555C23×C7C2×#4112yes—
556C23×C7C2511yescharacteristic
557C22×D7—22no—
558C22×D7—22no—
559C22×D7—22no—
560C22×D7—22no—
561C22×D7—28no—
562C22×D7—21no—
563C22×D7—21no—
564C22×D7—21no—
565C22×D7—21no—
566C22×D7—22no—
567C22×D7—22no—
568C22×D7—22no—
569C22×D7—22no—
570C22×D7—21no—
571C22×D7—21no—
572C22×D7—21no—
573C22×D7—22no—
574C22×D7—22no—
575C22×D7—44no—
576C22×D7—44no—
577C22×D7—44no—
578C22×D7—44no—
579C22×D7—48no—
580C22×D7—48no—
581C22×D7—48no—
582C22×D7—48no—
583C22×D7—48no—
584C22×D7—44no—
585C22×D7—82no—
586C22×D7—82no—
587C22×D7—84no—
588C22×D7#123116yescomplemented
589C22×D7C22×D412yes—
590C22×D7C22×D412yes—
591C22×D7C22×D412yes—
592C22×D7C22×D412yes—
593C22×D7C2×#4112yes—
594C22×D7C2×#4112yes—
595C22×D7C2×#4112yes—
596C22×D7C2×#4112yes—
597C7×D4—44no—
598C2×C4×C7—28no—
599C2×C4×C7—28no—
600C2×C4×C7—22no—
601C2×C4×C7—21no—
602C2×C4×C7—21no—
603C2×C4×C7—21no—
604C2×C4×C7—21no—
605C2×C4×C7—22no—
606C2×C4×C7—22no—
607C2×C4×C7—21no—
608C2×C4×C7—21no—
609C2×C4×C7—21no—
610C2×C4×C7—22no—
611C2×C4×C7—22no—
612C2×C4×C7—21no—
613C2×C4×C7—21no—
614C2×C4×C7—22no—
615C2×C4×C7—22no—
616C2×C4×C7—22no—
617C2×C4×C7—22no—
618C2×C4×C7—22no—
619C2×C4×C7—22no—
620C2×C4×C7—22no—
621C2×C4×C7—22no—
622C2×C4×C7—44no—
623C2×C4×C7C22×D412yes—
624C2×C4×C7C22×D412yes—
625C2×C4×C7H(5,𝔽2)14yes—
626C22⋊D7—44no—
627C22⋊D7—44no—
628C22⋊D7—82no—
629C22⋊D7—82no—
630C2×Dic7—21no—
631C2×Dic7—21no—
632C2×Dic7—21no—
633C2×Dic7—22no—
634C2×Dic7—22no—
635C2×Dic7—22no—
636C2×Dic7—22no—
637C2×Dic7—21no—
638C2×Dic7—21no—
639C2×Dic7—22no—
640C2×Dic7—22no—
641C2×Dic7—22no—
642C2×Dic7—22no—
643C2×Dic7—22no—
644C2×Dic7—22no—
645C2×Dic7—22no—
646C2×Dic7—22no—
647C2×Dic7—22no—
648C2×Dic7—22no—
649C2×Dic7—44no—
650C2×Dic7—44no—
651D28—28no—
652D28—28no—
653D28—28no—
654D28—28no—
655D28—44no—
656D28—82no—
657D28—82no—
658C4×D7—48no—
659C4×D7—48no—
660C4×D7—48no—
661C4×D7—48no—
662C4×D7—48no—
663C4×D7—44no—
664C4×D7—82no—
665C4×D7—82no—
666C4×D7—84no—
667C25—71no—
668C25—71no—
669C25—71no—
670C22×D4—71no—
671C22×D4—71no—
672C22×D4—71no—
673C22×D4—71no—
674C22×D4—78no—
675C22×D4—71no—
676C22×D4—71no—
677C22×D4—71no—
678C22×D4—71no—
679C22×D4—71no—
680C22×D4—71no—
681C22×D4—71no—
682C22×D4—144no—
683C22×D4—144no—
684C22×D4—144no—
685C22×D4—144no—
686C22×D4—144no—
687C22×D4C22×D711yescharacteristic
688C23×C4—71no—
689C23×C4—71no—
690C23×C4—71no—
691C23×C4—72no—
692C23×C4—72no—
693C23×C4—72no—
694C23×C4—72no—
695C23×C4—72no—
696C23×C4—71no—
697C23×C4—72no—
698C23×C4—71no—
699C23×C4—144no—
700C23×C4—144no—
701C23×C4—284no—
702C23×C4—284no—
703C23×C4C22×D711yescharacteristic
704C23×C4C22×D711yescharacteristic
705C23×C4C22×D711yescharacteristic
706#123—24no—
707#123—144no—
708#123—144no—
709#123—144no—
710#123—284no—
711#123—284no—
712#121—144no—
713#121—144no—
714#121—144no—
715#121—144no—
716#120—144no—
717#120—144no—
718#120—144no—
719#120—144no—
720C4×D4—148no—
721C4×D4—148no—
722C4×D4—148no—
723C4×D4—148no—
724C2×C4⋊C4—72no—
725C2×C4⋊C4—72no—
726C2×C4⋊C4—72no—
727C2×C4⋊C4—71no—
728C2×C4⋊C4—71no—
729C2×C4⋊C4—72no—
730C2×C4⋊C4—72no—
731C2×C4⋊C4—72no—
732C2×C4⋊C4—72no—
733C2×C4⋊C4—72no—
734C2×C4⋊C4—144no—
735C2×C4⋊C4—284no—
736C2×C4⋊C4C22×D712yes—
737C2×C4⋊C4C22×D711yescharacteristic
738C2×C4⋊C4C22×D711yescharacteristic
739C2×C4⋊C4C22×D712yes—
740C2×C22⋊C4—71no—
741C2×C22⋊C4—71no—
742C2×C22⋊C4—71no—
743C2×C22⋊C4—72no—
744C2×C22⋊C4—72no—
745C2×C22⋊C4—72no—
746C2×C22⋊C4—72no—
747C2×C22⋊C4—71no—
748C2×C22⋊C4—71no—
749C2×C22⋊C4—72no—
750C2×C22⋊C4—72no—
751C2×C22⋊C4—72no—
752C2×C22⋊C4—71no—
753C2×C22⋊C4—71no—
754C2×C22⋊C4—71no—
755C2×C22⋊C4—71no—
756C2×C22⋊C4—71no—
757C2×C22⋊C4—71no—
758C2×C22⋊C4—72no—
759C2×C22⋊C4—72no—
760C2×C22⋊C4—72no—
761C2×C22⋊C4—72no—
762C2×C22⋊C4—72no—
763C2×C22⋊C4—72no—
764C2×C22⋊C4—72no—
765C2×C22⋊C4—72no—
766C2×C22⋊C4—72no—
767C2×C22⋊C4—144no—
768C2×C22⋊C4—144no—
769C2×C22⋊C4—144no—
770C2×C22⋊C4—144no—
771C2×C22⋊C4—144no—
772C2×C22⋊C4—284no—
773C2×C22⋊C4C22×D711yescharacteristic
774C2×C22⋊C4C22×D712yes—
775C2×C22⋊C4C22×D711yescharacteristic
776C2×C22⋊C4C22×D711yescharacteristic
777C2×C22⋊C4C22×D711yescharacteristic
778C2×C22⋊C4C22×D711yescharacteristic
779C2×C22⋊C4C22×D712yes—
780C2×C42—24no—
781C2×C42C22×D712yes—
782C2×C42C22×D712yes—
783#95—72no—
784#95—72no—
785#95—72no—
786#95—72no—
787#95—72no—
788#95—72no—
789#95—72no—
790#95—72no—
791#95—72no—
792#95—72no—
793#95—72no—
794#95—72no—
795#95—72no—
796#95—72no—
797#95C22×D712yes—
798#95C22×D712yes—
799#95C22×D712yes—
800#95C22×D712yes—
801#95C22×D712yes—
802#95C22×D712yes—
803C22×C7—24no—
804C22×C7—22no—
805C22×C7—22no—
806C22×C7—24no—
807C22×C7—41no—
808C22×C7—42no—
809C22×C7—41no—
810C22×C7—41no—
811C22×C7—42no—
812C22×C7C2×#12314yes—
813C22×C7C23×D411yescharacteristic
814C22×C7C22×#4111yescharacteristic
815C22×C7C22×#4111yescharacteristic
816C22×C7C2×H(5,𝔽2)12yes—
817C22×C7#58512yes—
818C2×D7—24no—
819C2×D7—24no—
820C2×D7—22no—
821C2×D7—22no—
822C2×D7—22no—
823C2×D7—22no—
824C2×D7—24no—
825C2×D7—24no—
826C2×D7—22no—
827C2×D7—22no—
828C2×D7—22no—
829C2×D7—22no—
830C2×D7—22no—
831C2×D7—22no—
832C2×D7—416no—
833C2×D7—416no—
834C2×D7—42no—
835C2×D7—42no—
836C2×D7—42no—
837C2×D7—42no—
838C2×D7—41no—
839C2×D7—42no—
840C2×D7—41no—
841C2×D7—41no—
842C2×D7—42no—
843C2×D7—88no—
844C2×D7C2×#12314yes—
845C2×D7C2×#12314yes—
846C4×C7—22no—
847C4×C7—22no—
848C4×C7—24no—
849C4×C7—41no—
850C4×C7—42no—
851C4×C7—41no—
852C4×C7—41no—
853C4×C7—42no—
854C4×C7—42no—
855Dic7—41no—
856Dic7—42no—
857Dic7—42no—
858Dic7—42no—
859Dic7—41no—
860Dic7—41no—
861Dic7—42no—
862C24—71no—
863C24—71no—
864C24—74no—
865C24—74no—
866C24—74no—
867C24—71no—
868C24—71no—
869C24—74no—
870C24—71no—
871C24—142no—
872C24—142no—
873C24—142no—
874C24—142no—
875C24—142no—
876C24—282no—
877C24—282no—
878C24—282no—
879C24—282no—
880C24—282no—
881C24—282no—
882C24C23×D711yescharacteristic
883C24C23×D711yescharacteristic
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—74no—
888C2×D4—74no—
889C2×D4—74no—
890C2×D4—74no—
891C2×D4—1432no—
892C2×D4—142no—
893C2×D4—142no—
894C2×D4—142no—
895C2×D4—142no—
896C2×D4—142no—
897C2×D4—142no—
898C2×D4—142no—
899C2×D4—142no—
900C2×D4—142no—
901C2×D4—142no—
902C2×D4—142no—
903C2×D4—142no—
904C2×D4—142no—
905C2×D4—142no—
906C2×D4—142no—
907C2×D4—142no—
908C2×D4—142no—
909C2×D4—142no—
910C2×D4—142no—
911C2×D4—142no—
912C2×D4—142no—
913C2×D4—282no—
914C2×D4—282no—
915C2×D4—282no—
916C2×D4—282no—
917C2×D4—2816no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—24no—
922C22×C4—22no—
923C22×C4—42no—
924C22×C4—71no—
925C22×C4—72no—
926C22×C4—72no—
927C22×C4—71no—
928C22×C4—72no—
929C22×C4—72no—
930C22×C4—71no—
931C22×C4—144no—
932C22×C4—144no—
933C22×C4—144no—
934C22×C4—144no—
935C22×C4—144no—
936C22×C4—142no—
937C22×C4—142no—
938C22×C4—142no—
939C22×C4—142no—
940C22×C4—142no—
941C22×C4—144no—
942C22×C4—142no—
943C22×C4—142no—
944C22×C4—144no—
945C22×C4—144no—
946C22×C4—144no—
947C22×C4—144no—
948C22×C4—282no—
949C22×C4—282no—
950C22×C4—282no—
951C22×C4—282no—
952C22×C4—282no—
953C22×C4—282no—
954C22×C4—282no—
955C22×C4—282no—
956C22×C4—282no—
957C22×C4—282no—
958C22×C4—2816no—
959C22×C4—2816no—
960C22×C4—282no—
961C22×C4—282no—
962C22×C4D4×D714yes—
963C22×C4C23×D711yescharacteristic
964C22×C4C23×D711yescharacteristic
965C22×C4C23×D712yes—
966C22×C4C23×D712yes—
967C22×C4C23×D712yes—
968C22×C4C23×D711yescharacteristic
969C22×C4C23×D711yescharacteristic
970C22×C4C23×D711yescharacteristic
971C22×C4C23×D712yes—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—24no—
975C4⋊C4—42no—
976C4⋊C4—142no—
977C4⋊C4—142no—
978C4⋊C4—144no—
979C4⋊C4—144no—
980C4⋊C4—144no—
981C4⋊C4—282no—
982C4⋊C4—282no—
983C4⋊C4—282no—
984C4⋊C4—282no—
985C4⋊C4—282no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—24no—
992C22⋊C4—42no—
993C22⋊C4—144no—
994C22⋊C4—144no—
995C22⋊C4—144no—
996C22⋊C4—144no—
997C22⋊C4—144no—
998C22⋊C4—144no—
999C22⋊C4—142no—
1000C22⋊C4—142no—
1001C22⋊C4—142no—
1002C22⋊C4—142no—
1003C22⋊C4—142no—
1004C22⋊C4—142no—
1005C22⋊C4—142no—
1006C22⋊C4—142no—
1007C22⋊C4—142no—
1008C22⋊C4—142no—
1009C22⋊C4—142no—
1010C22⋊C4—144no—
1011C22⋊C4—282no—
1012C22⋊C4—282no—
1013C22⋊C4—282no—
1014C22⋊C4—282no—
1015C22⋊C4—282no—
1016C22⋊C4—282no—
1017C22⋊C4—282no—
1018C22⋊C4—282no—
1019C22⋊C4—282no—
1020C42—24no—
1021C42—24no—
1022C2×C7—24no—
1023C2×C7—81no—
1024C2×C7C22×#12311yescharacteristic
1025C2×C7#345912yes—
1026C2×C7#348411yescharacteristic
1027C2×C7#348511yescharacteristic
1028C2×C7#350512yes—
1029D7—24no—
1030D7—24no—
1031D7—42no—
1032D7—42no—
1033D7—81no—
1034C23—22no—
1035C23—22no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—22no—
1040C23—22no—
1041C23—72no—
1042C23—72no—
1043C23—72no—
1044C23—72no—
1045C23—72no—
1046C23—72no—
1047C23—716no—
1048C23—72no—
1049C23—72no—
1050C23—142no—
1051C23—142no—
1052C23—142no—
1053C23—142no—
1054C23—148no—
1055C23—141no—
1056C23—141no—
1057C23—141no—
1058C23—141no—
1059C23—142no—
1060C23—142no—
1061C23—142no—
1062C23—142no—
1063C23—141no—
1064C23—141no—
1065C23—141no—
1066C23—142no—
1067C23—142no—
1068C23—284no—
1069C23—284no—
1070C23—284no—
1071C23—284no—
1072C23—288no—
1073C23—288no—
1074C23—288no—
1075C23—288no—
1076C23—284no—
1077C23—288no—
1078C23—562no—
1079C23—562no—
1080C23—564no—
1081C23C2×D4×D712yes—
1082C23D7×#4112yes—
1083C23D7×#4112yes—
1084C23C24×D711yescharacteristic
1085D4—44no—
1086D4—148no—
1087D4—148no—
1088D4—148no—
1089D4—148no—
1090D4—284no—
1091D4—284no—
1092D4—284no—
1093D4—562no—
1094D4—562no—
1095D4—562no—
1096D4—562no—
1097C2×C4—28no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—44no—
1122C2×C4—141no—
1123C2×C4—141no—
1124C2×C4—142no—
1125C2×C4—142no—
1126C2×C4—141no—
1127C2×C4—142no—
1128C2×C4—142no—
1129C2×C4—141no—
1130C2×C4—141no—
1131C2×C4—142no—
1132C2×C4—142no—
1133C2×C4—142no—
1134C2×C4—142no—
1135C2×C4—142no—
1136C2×C4—142no—
1137C2×C4—142no—
1138C2×C4—142no—
1139C2×C4—142no—
1140C2×C4—142no—
1141C2×C4—288no—
1142C2×C4—288no—
1143C2×C4—288no—
1144C2×C4—288no—
1145C2×C4—284no—
1146C2×C4—288no—
1147C2×C4—284no—
1148C2×C4—284no—
1149C2×C4—562no—
1150C2×C4—562no—
1151C2×C4—564no—
1152C2×C4C2×D4×D712yes—
1153C2×C4C2×D4×D712yes—
1154C2×C4#655314yes—
1155C7#3498311yescharacteristic, complemented, Sylow
1156C22—22no—
1157C22—22no—
1158C22—24no—
1159C22—24no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—42no—
1164C22—42no—
1165C22—74no—
1166C22—74no—
1167C22—142no—
1168C22—142no—
1169C22—142no—
1170C22—142no—
1171C22—144no—
1172C22—144no—
1173C22—144no—
1174C22—144no—
1175C22—142no—
1176C22—142no—
1177C22—142no—
1178C22—142no—
1179C22—142no—
1180C22—142no—
1181C22—2816no—
1182C22—2816no—
1183C22—282no—
1184C22—282no—
1185C22—282no—
1186C22—282no—
1187C22—281no—
1188C22—281no—
1189C22—281no—
1190C22—282no—
1191C22—282no—
1192C22—568no—
1193C22D7×#12314yes—
1194C22C22×D4×D711yescharacteristic
1195C22C2×D7×#4111yescharacteristic
1196C22C2×D7×#4111yescharacteristic
1197C22C2×#655312yes—
1198C22#9061612yes—
1199C4—22no—
1200C4—22no—
1201C4—24no—
1202C4—41no—
1203C4—41no—
1204C4—42no—
1205C4—41no—
1206C4—42no—
1207C4—42no—
1208C4—281no—
1209C4—282no—
1210C4—282no—
1211C4—281no—
1212C4—281no—
1213C4—282no—
1214C4—282no—
1215C2—24no—
1216C2—81no—
1217C2—144no—
1218C2—144no—
1219C2—282no—
1220C2—282no—
1221C2—561no—
1222C2C2×D7×#12311yescharacteristic
1223C2#1174310711yescharacteristic
1224C2#1174310811yescharacteristic
1225C2#1174321512yes—
1226C2#1174322612yes—
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2853C2
prime radicalC2×#90344C2
hypercenter#2853D7
hypocenterC7#34983
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2853

Complements

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

NH ≅ G/Ntype
2. C22×C4×D28C2semidirect
3. C7×#2853C2semidirect
4. #11740311C2semidirect
5. #11739524C2semidirect
6. #11733294C2semidirect
7. #11733293C2semidirect
8. #11733290C2semidirect
9. #11733289C2semidirect
10. #11732765C2semidirect
11. #11732764C2semidirect
12. #11732761C2semidirect
13. #11732760C2semidirect
14. #11732381C2semidirect
15. #11732351C2semidirect
16. #11732319C2semidirect
17. D7×#386C2semidirect
18. #11732101C2semidirect
19. #11732064C2semidirect
20. #11732036C2semidirect
21. D7×#385C2semidirect
22. #11731581C2semidirect
23. #11731564C2semidirect
27. C23×C4×D7C22semidirect
29. C22×C42×C7C22semidirect
33. C22×(C2×D7)⋊C4C22semidirect
34. C22×C4⋊Dic7C22semidirect
40. C2×#6457C22semidirect
41. C2×D7×C4⋊C4C22semidirect
44. C2×#6446C22semidirect
51. C2×D7×C22⋊C4C22semidirect
55. C2×C4×D28C22semidirect
56. C2×C4×D28C22semidirect
57. C7×#388C22semidirect
58. C7×#388C22semidirect
59. C7×#387C22semidirect
60. C7×#387C22semidirect
63. C7×#385C22semidirect
64. C7×#385C22semidirect
65. C7×#381C22semidirect
70. #89983C22semidirect
71. #89982C22semidirect
72. #89982C22semidirect
73. #89765C22semidirect
74. #89763C22semidirect
75. #89761C22semidirect
76. #89761C22semidirect
77. #89761C22semidirect
78. #89759C22semidirect
79. #89758C22semidirect
80. #89755C22semidirect
81. #89733C22semidirect
82. #89731C22semidirect
85. #89728C22semidirect
86. #89728C22semidirect
87. #89728C22semidirect
88. #89727C22semidirect
89. #89727C22semidirect
90. #89727C22semidirect
91. #89725C22semidirect
92. #89722C22semidirect
93. #89722C22semidirect
94. #89721C22semidirect
95. #89718C22semidirect
96. #89718C22semidirect
97. #89712C22semidirect
98. #89712C22semidirect
99. #89705C22semidirect
100. #89705C22semidirect
101. #89449C22semidirect
102. #89447C22semidirect
103. #89447C22semidirect
104. #89446C22semidirect
105. #89446C22semidirect
106. #89444C22semidirect
107. #89440C22semidirect
108. #89440C22semidirect
109. #89440C22semidirect
110. #89439C22semidirect
113. #89437C22semidirect
114. #89437C22semidirect
115. #89437C22semidirect
116. #89437C22semidirect
117. #89437C22semidirect
118. #89436C22semidirect
119. #89436C22semidirect
120. #89436C22semidirect
121. D7×#95C22semidirect
122. D7×#95C22semidirect
123. #89433C22semidirect
124. #89431C22semidirect
265. #2853D7semidirect
477. C22×C42C2×D7semidirect
496. #388C2×D7semidirect
497. #388C2×D7semidirect
500. #387C2×D7semidirect
501. #387C2×D7semidirect
532. #385C2×D7semidirect
533. #385C2×D7semidirect
538. #381C2×D7semidirect
588. C22×D7#123semidirect
1155. C7#34983semidirect

Maximal subgroups

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

subgroupindex
C2×#903442
C22×C4×D282
C7×#28532
#117403112
#117395242
#117332942
#117332932
#117332902
#117332892
#117327652
#117327642
#117327612
#117327602
#117323812
#117323512
#117323192
D7×#3862
#117321012
#117320642
#117320362
D7×#3852
#117315812
#117315642
#349837