Finite Group Databasebeta

← C2×#11735391 #13522491

Subgroups — C2×#11735391 #13522491

Order 1792.

3570 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6457C211yesmaximal, characteristic
2C22×#6457C211yesmaximal, characteristic
3C22×D7×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×#6455C211yesmaximal, characteristic, complemented
5C2×C7×#398C211yesmaximal, characteristic, complemented
6C2×#89766C211yesmaximal, characteristic, complemented
7C2×#89766C211yesmaximal, characteristic, complemented
8C2×#89756C211yesmaximal, characteristic, complemented
9C2×#89745C211yesmaximal, characteristic, complemented
10#11735391C2116yesmaximal, direct product factor
11C2×#89437C211yesmaximal, characteristic
12C2×#89440C211yesmaximal, characteristic, complemented
13C2×#89436C211yesmaximal, characteristic, complemented
14C2×#89419C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89441C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6457—28no—
45C2×#6457—28no—
46C2×#6457C2218yes—
47C2×#6457C2218yes—
48C2×#6455—28no—
49C2×#6455C2218yescomplemented
50C2×D7×C4⋊C4—28no—
51C2×D7×C4⋊C4C2218yescomplemented
52C7×#398C2218yescomplemented
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89766C2218yescomplemented
62#89766C2218yescomplemented
63#89756C2218yescomplemented
64#89745C2218yescomplemented
65#89442C2218yescomplemented
66#89441C2218yescomplemented
67#89440C2218yescomplemented
68#89437C2218yes—
69#89436C2218yescomplemented
70#89419C2218yescomplemented
71C2×#2413—71nomaximal, Sylow
72C24×D7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C22×D28—24no—
88C22×D28—24no—
89C22×D28—24no—
90C22×D28C2314yes—
91C22×C4×D7—24no—
92C22×C4×D7—24no—
93C22×C4×D7—24no—
94C22×C4×D7—24no—
95C22×C4×D7—24no—
96C22×C4×D7—24no—
97C22×C4×D7—24no—
98C22×C4×D7—24no—
99C22×C4×D7D418yes—
100C22×C4×D7C2314yes—
101C22×C4×D7C2314yes—
102C22×C4×D7C2314yes—
103C2×C7×C4⋊C4—24no—
104C2×C7×C4⋊C4—24no—
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4—24no—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C4⋊C4C2314yes—
110C2×C7×C4⋊C4C2314yes—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4D418yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×C4⋊Dic7—24no—
130C2×C4⋊Dic7—24no—
131C2×C4⋊Dic7—24no—
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134C2×C4⋊Dic7C2314yes—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×C4×Dic7—24no—
146C2×C4×Dic7—24no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149#6457—232no—
150#6457—232no—
151#6455—232no—
152D7×C4⋊C4—232no—
153C7×#95C2314yes—
154C7×#95C2314yes—
155C7×#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C22×#123—71no—
162C22×#123—71no—
163C22×#117—71no—
164C23×C4⋊C4—71no—
165#2413—716no—
166C2×#398—71no—
167C2×#398D711yescharacteristic, complemented
168C2×#396—71no—
169C2×#396—71no—
170C2×#389—71no—
171C2×#389—71no—
172C2×#388—71no—
173C2×#388—71no—
174C2×#386—71no—
175C2×#385—71no—
176C2×#381—71no—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7C2×D414yes—
190C23×D7C2×D414yes—
191C23×D7#4114yes—
192C23×D7C2412yes—
193C23×D7C2412yes—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7C2×D414yes—
213C22×C4×C7C2×D414yes—
214C22×C4×C7#4114yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7C2×D414yes—
238C22×Dic7C2×D414yes—
239C22×Dic7#4114yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C2×D28—28no—
247C2×D28—28no—
248C2×D28—28no—
249C2×D28—416no—
250C2×C4×D7—232no—
251C2×C4×D7—232no—
252C2×C4×D7—28no—
253C2×C4×D7—28no—
254C2×C4×D7—28no—
255C2×C4×D7—28no—
256C2×C4×D7—28no—
257C2×C4×D7—28no—
258C2×C4×D7—28no—
259C2×C4×D7—28no—
260C2×C4×D7—416no—
261C2×C4×D7C2×D4116yes—
262C7×C4⋊C4—28no—
263C7×C4⋊C4—28no—
264C7×C4⋊C4—28no—
265C7×C4⋊C4—28no—
266(C2×D7)⋊C4—28no—
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—28no—
269(C2×D7)⋊C4—28no—
270(C2×D7)⋊C4—28no—
271(C2×D7)⋊C4—28no—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4—28no—
274(C2×D7)⋊C4C2×D4116yes—
275C4⋊Dic7—28no—
276C4⋊Dic7—28no—
277C4⋊Dic7—28no—
278Dic7⋊C4—28no—
279Dic7⋊C4—28no—
280Dic7⋊C4—28no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283C4×Dic7—28no—
284C4×Dic7—28no—
285C23×D4—71no—
286C24×C4—71no—
287C24×C4—71no—
288C24×C4—71no—
289C2×#123—78no—
290C2×#123—78no—
291C2×#123—148no—
292C2×#123—148no—
293C2×#117—78no—
294C2×#117—148no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—78no—
304C22×C4⋊C4—148no—
305C22×C4⋊C4C2×D711yescharacteristic
306C22×C4⋊C4C2×D711yescharacteristic
307C22×C4⋊C4C2×D711yescharacteristic
308C22×C4⋊C4C2×D711yescharacteristic
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C42—71no—
319C22×C42—71no—
320#398—78no—
321#398C2×D718yescomplemented
322#396—78no—
323#396—78no—
324#389—78no—
325#389—78no—
326#388—78no—
327#388—78no—
328#386—78no—
329#385—78no—
330#381—78no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95C2×D711yescharacteristic
337C2×#95C2×D711yescharacteristic
338C2×#95C2×D711yescharacteristic
339C23×C7C22×D412yes—
340C23×C7C22×D412yes—
341C23×C7C2×#4112yes—
342C23×C7C2×#4112yes—
343C23×C7C2×#4112yes—
344C23×C72−1+412yes—
345C23×C72−1+412yes—
346C23×C7C2511yescharacteristic
347C22×D7—28no—
348C22×D7—28no—
349C22×D7—28no—
350C22×D7—28no—
351C22×D7—28no—
352C22×D7—28no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—44no—
365C22×D7—44no—
366C22×D7—44no—
367C22×D7—44no—
368C22×D7—44no—
369C22×D7—44no—
370C22×D7—44no—
371C22×D7#121116yes—
372C22×D7C22×D414yes—
373C22×D7C22×D414yes—
374C22×D7C2×#4114yes—
375C2×C4×C7—28no—
376C2×C4×C7—28no—
377C2×C4×C7—28no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C2×C4×C7—44no—
399C2×C4×C7—44no—
400C2×C4×C7C22×D414yes—
401C2×C4×C7C22×D414yes—
402C2×C4×C7C2×#4114yes—
403C2×Dic7—28no—
404C2×Dic7—28no—
405C2×Dic7—28no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—44no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7C22×D414yes—
425C2×Dic7C22×D414yes—
426C2×Dic7C2×#4114yes—
427D28—416no—
428C4×D7—232no—
429C4×D7—232no—
430C4×D7—416no—
431C25—71no—
432C25—71no—
433C22×D4—74no—
434C22×D4—144no—
435C22×D4—144no—
436C22×D4—144no—
437C23×C4—71no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—78no—
441C23×C4—74no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—74no—
446C23×C4—74no—
447C23×C4—144no—
448C23×C4—144no—
449C23×C4—144no—
450C23×C4—144no—
451C23×C4—144no—
452C23×C4—144no—
453C23×C4—144no—
454C23×C4—144no—
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C23×C4C22×D711yescharacteristic
461C23×C4C22×D711yescharacteristic
462#123—1432no—
463#123—1432no—
464#117—1432no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—74no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—1432no—
478C2×C4⋊C4—144no—
479C2×C4⋊C4—144no—
480C2×C4⋊C4—144no—
481C2×C4⋊C4—144no—
482C2×C4⋊C4—144no—
483C2×C4⋊C4—144no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4C22×D714yes—
487C2×C4⋊C4C22×D714yes—
488C2×C4⋊C4C22×D714yes—
489C2×C4⋊C4C22×D714yes—
490C2×C22⋊C4—78no—
491C2×C22⋊C4—74no—
492C2×C22⋊C4—74no—
493C2×C22⋊C4—74no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—144no—
501C2×C22⋊C4—144no—
502C2×C22⋊C4—144no—
503C2×C22⋊C4—144no—
504C2×C22⋊C4—144no—
505C2×C22⋊C4—144no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C42—74no—
509C2×C42—74no—
510C2×C42—144no—
511C2×C42—144no—
512#95—74no—
513#95—74no—
514#95—74no—
515#95—74no—
516#95—74no—
517#95C22×D714yes—
518#95C22×D714yes—
519#95C22×D714yes—
520C22×C7C2×#12114yes—
521C22×C7#52514yes—
522C22×C7#53614yes—
523C22×C7#54714yes—
524C22×C7#54714yes—
525C22×C7#55214yes—
526C22×C7#55214yes—
527C22×C7C23×D411yescharacteristic
528C22×C7C23×D411yescharacteristic
529C22×C7C22×#4111yescharacteristic
530C22×C7C22×#4111yescharacteristic
531C22×C7C22×#4111yescharacteristic
532C22×C7C2×2−1+411yescharacteristic
533C22×C7C2×2−1+411yescharacteristic
534C2×D7—24no—
535C2×D7—232no—
536C2×D7—24no—
537C2×D7—24no—
538C2×D7—24no—
539C2×D7—24no—
540C2×D7—24no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—88no—
549C2×D7C2×#12118yes—
550C4×C7—24no—
551C4×C7—24no—
552C4×C7—24no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7—42no—
556C4×C7—42no—
557Dic7—24no—
558Dic7—24no—
559Dic7—24no—
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563C24—74no—
564C24—74no—
565C24—74no—
566C24—72no—
567C24—72no—
568C24—142no—
569C24—142no—
570C24—142no—
571C24—142no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24—142no—
576C24—142no—
577C24—142no—
578C24—142no—
579C24C23×D711yescharacteristic
580C2×D4—148no—
581C2×D4—148no—
582C2×D4—148no—
583C2×D4—2816no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—74no—
603C22×C4—74no—
604C22×C4—74no—
605C22×C4—72no—
606C22×C4—72no—
607C22×C4—72no—
608C22×C4—716no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—148no—
613C22×C4—148no—
614C22×C4—148no—
615C22×C4—1432no—
616C22×C4—148no—
617C22×C4—1432no—
618C22×C4—148no—
619C22×C4—148no—
620C22×C4—148no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—148no—
628C22×C4—142no—
629C22×C4—142no—
630C22×C4—142no—
631C22×C4—142no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—142no—
635C22×C4—142no—
636C22×C4—142no—
637C22×C4—2816no—
638C22×C4D4×D714yes—
639C22×C4D4×D714yes—
640C22×C4#116114yes—
641C22×C4C23×D712yes—
642C22×C4C23×D712yes—
643C22×C4C23×D712yes—
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—148no—
653C4⋊C4—148no—
654C4⋊C4—148no—
655C4⋊C4—148no—
656C4⋊C4—148no—
657C4⋊C4—148no—
658C4⋊C4—148no—
659C4⋊C4—148no—
660C22⋊C4—716no—
661C22⋊C4—148no—
662C22⋊C4—148no—
663C22⋊C4—148no—
664C22⋊C4—148no—
665C22⋊C4—148no—
666C22⋊C4—148no—
667C22⋊C4—148no—
668C22⋊C4—148no—
669C42—148no—
670C42—148no—
671C2×C7#241318yescomplemented
672C2×C7C22×#12111yescharacteristic
673C2×C7C2×#52511yescharacteristic
674C2×C7C2×#53611yescharacteristic
675C2×C7C2×#54711yescharacteristic
676C2×C7C2×#54711yescharacteristic
677C2×C7C2×#55211yescharacteristic
678C2×C7C2×#55211yescharacteristic
679D7—28no—
680D7—82no—
681C23—716no—
682C23—74no—
683C23—74no—
684C23—74no—
685C23—148no—
686C23—148no—
687C23—148no—
688C23—148no—
689C23—148no—
690C23—148no—
691C23—142no—
692C23—142no—
693C23—142no—
694C23—142no—
695C23—142no—
696C23—142no—
697C23—142no—
698C23—142no—
699C23—142no—
700C23—142no—
701C23—142no—
702C23—284no—
703C23—284no—
704C23—284no—
705C23—284no—
706C23—284no—
707C23—284no—
708C23—284no—
709C23C2×D4×D712yes—
710C23C2×D4×D712yes—
711C23C2×#116112yes—
712C23#655112yes—
713C23D7×#4112yes—
714C23D7×#4112yes—
715C23#655412yes—
716C23C24×D711yescharacteristic
717D4—2816no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—74no—
744C2×C4—74no—
745C2×C4—74no—
746C2×C4—1432no—
747C2×C4—1432no—
748C2×C4—148no—
749C2×C4—148no—
750C2×C4—148no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—2816no—
767C2×C4—284no—
768C2×C4—284no—
769C2×C4—284no—
770C2×C4C2×D4×D714yes—
771C2×C4C2×D4×D714yes—
772C2×C4C2×#116114yes—
773C7C2×#241311yescharacteristic, complemented, Sylow
774C22—78no—
775C22—144no—
776C22—144no—
777C22—144no—
778C22—1432no—
779C22—144no—
780C22—144no—
781C22—144no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—282no—
786C22—282no—
787C22—282no—
788C22—282no—
789C22—568no—
790C22D7×#12114yes—
791C22#9031814yes—
792C22#9031914yes—
793C22#9034614yes—
794C22#9038414yes—
795C22#9038514yes—
796C22#9041714yes—
797C22C22×D4×D711yescharacteristic
798C22C22×D4×D711yescharacteristic
799C22C22×#116111yescharacteristic
800C22C2×#655111yescharacteristic
801C22C2×D7×#4111yescharacteristic
802C22C2×D7×#4111yescharacteristic
803C22C2×#655411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—144no—
812C4—144no—
813C4—144no—
814C4—282no—
815C4—282no—
816C4—282no—
817C2—148no—
818C2—562no—
819C2#1173539118yesdirect product factor
820C2C2×D7×#12111yescharacteristic
821C2C2×#9031811yescharacteristic
822C2C2×#9031911yescharacteristic
823C2C2×#9034611yescharacteristic
824C2C2×#9038411yescharacteristic
825C2C2×#9038511yescharacteristic
826C2C2×#9041711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#398C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#398D7
hypocenterC7C2×#2413
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. C22×D7×C4⋊C4C2semidirect
4. C22×#6455C2semidirect
5. C2×C7×#398C2semidirect
6. C2×#89766C2semidirect
7. C2×#89766C2semidirect
8. C2×#89756C2semidirect
9. C2×#89745C2semidirect
10. #11735391C2direct (N × H)
12. C2×#89440C2semidirect
13. C2×#89436C2semidirect
14. C2×#89419C2semidirect
15. C2×#89442C2semidirect
16. C2×#89441C2semidirect
49. C2×#6455C22semidirect
51. C2×D7×C4⋊C4C22semidirect
52. C7×#398C22semidirect
61. #89766C22semidirect
62. #89766C22semidirect
63. #89756C22semidirect
64. #89745C22semidirect
65. #89442C22semidirect
66. #89441C22semidirect
67. #89440C22semidirect
69. #89436C22semidirect
70. #89419C22semidirect
167. C2×#398D7semidirect
321. #398C2×D7semidirect
671. C2×C7#2413semidirect
773. C7C2×#2413semidirect
819. C2#11735391direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64572
C22×D7×C4⋊C42
C22×#64552
C2×C7×#3982
C2×#897662
C2×#897562
C2×#897452
#117353912
C2×#894372
C2×#894402
C2×#894362
C2×#894192
C2×#894422
C2×#894412
C2×#24137