Finite Group Databasebeta

← C2×#11734736 #13521960

Subgroups — C2×#11734736 #13521960

Order 1792.

3094 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6452C211yesmaximal, characteristic, complemented
2C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic
3C2×C7×#396C211yesmaximal, characteristic, complemented
4C2×#89764C211yesmaximal, characteristic, complemented
5C2×#89761C211yesmaximal, characteristic, complemented
6C2×#89759C211yesmaximal, characteristic, complemented
7C2×#89744C211yesmaximal, characteristic, complemented
8C2×#89744C211yesmaximal, characteristic, complemented
9C2×#89721C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic
11C2×#89729C211yesmaximal, characteristic
12C2×#89718C211yesmaximal, characteristic, complemented
13C2×#89714C211yesmaximal, characteristic, complemented
14#11734736C2116yesmaximal, direct product factor
15C2×#89448C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6452—28no—
47C2×#6452C2218yescomplemented
48C2×(C22⋊D7)⋊C4—28no—
49C2×(C22⋊D7)⋊C4C2218yes—
50C7×#396C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89764C2218yescomplemented
58#89761C2218yescomplemented
59#89759C2218yescomplemented
60#89744C2218yescomplemented
61#89744C2218yescomplemented
62#89729C2218yes—
63#89729C2218yes—
64#89721C2218yescomplemented
65#89718C2218yescomplemented
66#89714C2218yescomplemented
67#89448C2218yescomplemented
68#89421C2218yescomplemented
69C2×#2454—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C22×C22⋊D7—24no—
79C22×C22⋊D7—24no—
80C22×C22⋊D7Q818yes—
81C22×C22⋊D7C2314yes—
82C23×Dic7—24no—
83C23×Dic7—24no—
84C23×Dic7—42no—
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2314yes—
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C22×C4×D7—24no—
94C22×C4×D7—24no—
95C22×C4×D7—42no—
96C22×C4×D7C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—42no—
99C2×C7×C4⋊C4—42no—
100C2×C7×C4⋊C4C2314yes—
101C2×C7×C4⋊C4C2314yes—
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—42no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4C2314yes—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—42no—
116C2×(C2×D7)⋊C4—42no—
117C2×(C2×D7)⋊C4—42no—
118C2×(C2×D7)⋊C4C2314yes—
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×C4⋊Dic7—24no—
124C2×C4⋊Dic7C2314yes—
125C2×Dic7⋊C4—24no—
126C2×Dic7⋊C4—24no—
127C2×Dic7⋊C4—24no—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—42no—
132C2×Dic7⋊C4—42no—
133C2×Dic7⋊C4D418yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7—24no—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—24no—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149#6452—232no—
150(C22⋊D7)⋊C4—232no—
151C7×#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C22×#125—71no—
158C22×C4×D4—71no—
159#2454—716no—
160C2×#399—71no—
161C2×#399—71no—
162C2×#396—71no—
163C2×#396D711yescharacteristic, complemented
164C2×#390—71no—
165C2×#390—71no—
166C2×#389—71no—
167C2×#389—71no—
168C2×#385—71no—
169C2×#385—71no—
170C2×#380—71no—
171C2×#380—71no—
172C2×C4×C4⋊C4—71no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7C2×Q814yes—
180C24×C7C2412yes—
181C24×C7C2411yescharacteristic
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7C2×Q814yes—
189C23×D7C2412yes—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
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×C7C2×D414yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C2×C22⋊D7—232no—
215C2×C22⋊D7—28no—
216C2×C22⋊D7—28no—
217C2×C22⋊D7C2×Q8116yes—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
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—28no—
234C22×Dic7—28no—
235C22×Dic7—44no—
236C22×Dic7—416no—
237C22×Dic7C2×D414yes—
238C22×Dic7C2×D414yes—
239C22×Dic7C2×Q814yes—
240C22×Dic7#4114yes—
241C22×Dic7#4114yes—
242C22×Dic7#4114yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C2×C4×D7—28no—
251C2×C4×D7—28no—
252C2×C4×D7—44no—
253C2×C4×D7—416no—
254C7×C4⋊C4—28no—
255C7×C4⋊C4—44no—
256C7×C4⋊C4—44no—
257C7×C22⋊C4—28no—
258C7×C22⋊C4—44no—
259C7×C22⋊C4—44no—
260C22⋊Dic7—28no—
261C22⋊Dic7—44no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—28no—
264(C2×D7)⋊C4—44no—
265(C2×D7)⋊C4—44no—
266(C2×D7)⋊C4—44no—
267C4⋊Dic7—28no—
268Dic7⋊C4—28no—
269Dic7⋊C4—28no—
270Dic7⋊C4—28no—
271Dic7⋊C4—28no—
272Dic7⋊C4—28no—
273Dic7⋊C4—28no—
274Dic7⋊C4—44no—
275Dic7⋊C4—44no—
276Dic7⋊C4C2×D4116yes—
277C4×Dic7—28no—
278C4×Dic7—28no—
279C4×Dic7—28no—
280C23×D4—71no—
281C24×C4—71no—
282C24×C4—71no—
283C2×#125—78no—
284C2×#125—148no—
285C2×C4×D4—78no—
286C2×C4×D4—148no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C4⋊C4C2×D711yescharacteristic
298C22×C4⋊C4C2×D711yescharacteristic
299C22×C4⋊C4C2×D711yescharacteristic
300C22×C22⋊C4—71no—
301C22×C22⋊C4—71no—
302C22×C22⋊C4—71no—
303C22×C22⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4C2×D711yescharacteristic
308C22×C22⋊C4C2×D711yescharacteristic
309C22×C22⋊C4C2×D711yescharacteristic
310C22×C42—71no—
311C22×C42—71no—
312C22×C42—71no—
313#399—78no—
314#399—78no—
315#396—78no—
316#396C2×D718yescomplemented
317#390—78no—
318#390—78no—
319#389—78no—
320#389—78no—
321#385—78no—
322#385—78no—
323#380—78no—
324#380—78no—
325C4×C4⋊C4—78no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95C2×D711yescharacteristic
332C23×C7—28no—
333C23×C7—28no—
334C23×C7—28no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—44no—
342C23×C7—44no—
343C23×C7—44no—
344C23×C7—44no—
345C23×C7C22×D412yes—
346C23×C7C22×Q814yes—
347C23×C7C22×Q812yes—
348C23×C7C2×#4112yes—
349C23×C7C2×#4112yes—
350C23×C7C2×#4112yes—
351C23×C7H(5,𝔽2)12yes—
352C23×C7H(5,𝔽2)12yes—
353C23×C7C2511yescharacteristic
354C22×D7—28no—
355C22×D7—28no—
356C22×D7—28no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—44no—
364C22×D7—44no—
365C22×D7—44no—
366C22×D7—44no—
367C22×D7C22×Q814yes—
368C2×C4×C7—28no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
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—44no—
387C2×C4×C7—44no—
388C2×C4×C7—44no—
389C2×C4×C7—44no—
390C2×C4×C7—44no—
391C2×C4×C7C22×D414yes—
392C22⋊D7—232no—
393C2×Dic7—28no—
394C2×Dic7—28no—
395C2×Dic7—28no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—416no—
412C2×Dic7—44no—
413C2×Dic7—44no—
414C2×Dic7—44no—
415C2×Dic7C22⋊Q8116yes—
416C2×Dic7C22×D414yes—
417C2×Dic7C22×D414yes—
418C2×Dic7C22×Q814yes—
419C2×Dic7C2×#4114yes—
420C2×Dic7C2×#4114yes—
421C2×Dic7C2×#4114yes—
422C4×D7—416no—
423C25—71no—
424C25C22×D711yescharacteristic
425C22×D4—78no—
426C22×D4—74no—
427C22×D4—144no—
428C22×D4—144no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—74no—
437C23×C4—74no—
438C23×C4—144no—
439C23×C4—144no—
440C23×C4—144no—
441C23×C4—144no—
442C23×C4—282no—
443C23×C4—282no—
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448C23×C4C22×D711yescharacteristic
449C23×C4C22×D711yescharacteristic
450#125—1432no—
451C4×D4—1432no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—78no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—144no—
467C2×C4⋊C4—144no—
468C2×C4⋊C4—144no—
469C2×C4⋊C4—144no—
470C2×C4⋊C4—144no—
471C2×C4⋊C4—144no—
472C2×C4⋊C4—144no—
473C2×C4⋊C4—282no—
474C2×C4⋊C4—282no—
475C2×C4⋊C4C22×D714yes—
476C2×C4⋊C4C22×D714yes—
477C2×C4⋊C4C22×D714yes—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—74no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—74no—
485C2×C22⋊C4—74no—
486C2×C22⋊C4—74no—
487C2×C22⋊C4—74no—
488C2×C22⋊C4—144no—
489C2×C22⋊C4—144no—
490C2×C22⋊C4—144no—
491C2×C22⋊C4—282no—
492C2×C22⋊C4—282no—
493C2×C22⋊C4—282no—
494C2×C22⋊C4—282no—
495C2×C22⋊C4C22×D714yes—
496C2×C22⋊C4C22×D714yes—
497C2×C22⋊C4C22×D714yes—
498C2×C42—74no—
499C2×C42—74no—
500C2×C42—74no—
501C2×C42—144no—
502C2×C42—144no—
503C2×C42—144no—
504#95—74no—
505#95—74no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95C22×D714yes—
510C22×C7—24no—
511C22×C7—24no—
512C22×C7—24no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7—416no—
518C22×C7C2×C22⋊Q814yes—
519C22×C7#52914yes—
520C22×C7#54014yes—
521C22×C7#54614yes—
522C22×C7#55014yes—
523C22×C7#55414yes—
524C22×C7#55414yes—
525C22×C7C23×D411yescharacteristic
526C22×C7C23×Q811yescharacteristic
527C22×C7C22×#4111yescharacteristic
528C22×C7C22×#4111yescharacteristic
529C22×C7C22×#4111yescharacteristic
530C22×C7C2×H(5,𝔽2)11yescharacteristic
531C22×C7C2×H(5,𝔽2)11yescharacteristic
532C2×D7—24no—
533C2×D7—24no—
534C2×D7—24no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—42no—
539C2×D7—416no—
540C4×C7—24no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7—42no—
544C4×C7—42no—
545C4×C7—42no—
546Dic7—24no—
547Dic7—24no—
548Dic7—24no—
549Dic7—42no—
550Dic7—42no—
551Dic7—42no—
552Dic7C2×C22⋊Q818yes—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—74no—
560C24—72no—
561C24—142no—
562C24—142no—
563C24—142no—
564C24—142no—
565C24—142no—
566C24—142no—
567C24Q8×D714yes—
568C24C23×D712yes—
569C24C23×D711yescharacteristic
570C2×D4—716no—
571C2×D4—148no—
572C2×D4—1432no—
573C2×D4—148no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—74no—
592C22×C4—74no—
593C22×C4—74no—
594C22×C4—72no—
595C22×C4—74no—
596C22×C4—74no—
597C22×C4—74no—
598C22×C4—72no—
599C22×C4—72no—
600C22×C4—72no—
601C22×C4—72no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—148no—
605C22×C4—148no—
606C22×C4—148no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—148no—
623C22×C4—284no—
624C22×C4—2816no—
625C22×C4—284no—
626C22×C4—2816no—
627C22×C4D4×D714yes—
628C22×C4C23×D712yes—
629C22×C4C23×D712yes—
630C22×C4C23×D712yes—
631C22×C4C23×D712yes—
632C22×C4C23×D712yes—
633C22×C4C23×D712yes—
634C4⋊C4—28no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—716no—
638C4⋊C4—148no—
639C4⋊C4—148no—
640C4⋊C4—148no—
641C4⋊C4—148no—
642C4⋊C4—148no—
643C4⋊C4—148no—
644C4⋊C4—148no—
645C4⋊C4—284no—
646C4⋊C4—284no—
647C22⋊C4—28no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—148no—
651C22⋊C4—148no—
652C22⋊C4—148no—
653C22⋊C4—284no—
654C22⋊C4—284no—
655C22⋊C4—284no—
656C22⋊C4—284no—
657C42—148no—
658C42—148no—
659C42—148no—
660C2×C7—44no—
661C2×C7#245418yescomplemented
662C2×C7C22×C22⋊Q811yescharacteristic
663C2×C7C2×#52911yescharacteristic
664C2×C7C2×#54011yescharacteristic
665C2×C7C2×#54611yescharacteristic
666C2×C7C2×#55011yescharacteristic
667C2×C7C2×#55411yescharacteristic
668C2×C7C2×#55411yescharacteristic
669D7—44no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—74no—
684C23—148no—
685C23—148no—
686C23—148no—
687C23—142no—
688C23—142no—
689C23—142no—
690C23—142no—
691C23—142no—
692C23—142no—
693C23—284no—
694C23—284no—
695C23—284no—
696C23—284no—
697C23C2×D4×D712yes—
698C23#654812yes—
699C23#654812yes—
700C23C2×Q8×D714yes—
701C23C2×Q8×D712yes—
702C23D7×#4112yes—
703C23D7×#4112yes—
704C23D7×#4112yes—
705C23C24×D711yescharacteristic
706D4—1432no—
707C2×C4—28no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—716no—
731C2×C4—74no—
732C2×C4—74no—
733C2×C4—74no—
734C2×C4—74no—
735C2×C4—74no—
736C2×C4—74no—
737C2×C4—148no—
738C2×C4—148no—
739C2×C4—148no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—2816no—
756C2×C4—2816no—
757C2×C4—284no—
758C2×C4—284no—
759C2×C4—284no—
760C2×C4C2×D4×D714yes—
761C7C2×#245411yescharacteristic, complemented, Sylow
762C22—24no—
763C22—24no—
764C22—24no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—416no—
770C22—144no—
771C22—144no—
772C22—144no—
773C22—282no—
774C22—282no—
775C22—282no—
776C22—282no—
777C22—2816no—
778C22#9029014yes—
779C22#9030114yes—
780C22#9030614yes—
781C22D7×C22⋊Q814yes—
782C22#9032714yes—
783C22#9032714yes—
784C22#9039714yes—
785C22C22×D4×D711yescharacteristic
786C22C2×#654811yescharacteristic
787C22C2×#654811yescharacteristic
788C22C22×Q8×D711yescharacteristic
789C22C2×D7×#4111yescharacteristic
790C22C2×D7×#4111yescharacteristic
791C22C2×D7×#4111yescharacteristic
792C4—24no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—78no—
799C4—144no—
800C4—144no—
801C4—144no—
802C4—282no—
803C4—282no—
804C4—282no—
805C2—44no—
806C2—284no—
807C2#1173473618yesdirect product factor
808C2C2×#9030611yescharacteristic
809C2C2×#9029011yescharacteristic
810C2C2×#9030111yescharacteristic
811C2C2×#9032711yescharacteristic
812C2C2×#9032711yescharacteristic
813C2C2×D7×C22⋊Q811yescharacteristic
814C2C2×#9039711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#396D7
hypocenterC7C2×#2454
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#6452C2semidirect
3. C2×C7×#396C2semidirect
4. C2×#89764C2semidirect
5. C2×#89761C2semidirect
6. C2×#89759C2semidirect
7. C2×#89744C2semidirect
8. C2×#89744C2semidirect
9. C2×#89721C2semidirect
12. C2×#89718C2semidirect
13. C2×#89714C2semidirect
14. #11734736C2direct (N × H)
15. C2×#89448C2semidirect
16. C2×#89421C2semidirect
47. C2×#6452C22semidirect
50. C7×#396C22semidirect
57. #89764C22semidirect
58. #89761C22semidirect
59. #89759C22semidirect
60. #89744C22semidirect
61. #89744C22semidirect
64. #89721C22semidirect
65. #89718C22semidirect
66. #89714C22semidirect
67. #89448C22semidirect
68. #89421C22semidirect
163. C2×#396D7semidirect
316. #396C2×D7semidirect
661. C2×C7#2454semidirect
761. C7C2×#2454semidirect
807. C2#11734736direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64522
C22×(C22⋊D7)⋊C42
C2×C7×#3962
C2×#897642
C2×#897612
C2×#897592
C2×#897442
C2×#897212
C2×#897292
C2×#897182
C2×#897142
#117347362
C2×#894482
C2×#894212
C2×#24547