Finite Group Databasebeta

← C2×#11732312 #13560000

Subgroups — C2×#11732312 #13560000

Order 1792.

2542 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#386C211yesmaximal, characteristic, complemented
2C2×#89995C211yesmaximal, characteristic
3C2×#89994C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5C2×#89982C211yesmaximal, characteristic, complemented
6C2×#89731C211yesmaximal, characteristic, complemented
7C2×#89721C211yesmaximal, characteristic, complemented
8C2×#89724C211yesmaximal, characteristic, complemented
9C2×#89720C211yesmaximal, characteristic, complemented
10C2×#89733C211yesmaximal, characteristic, complemented
11C2×#89733C211yesmaximal, characteristic, complemented
12#11732312C2116yesmaximal, direct product factor
13C2×#89447C211yesmaximal, characteristic, complemented
14C2×#89448C211yesmaximal, characteristic, complemented
15C2×#89431C211yesmaximal, characteristic, complemented
16C2×#89432C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C7×#386C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45#89995C2218yes—
46#89994C2218yescomplemented
47#89985C2218yescomplemented
48#89982C2218yescomplemented
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89733C2218yescomplemented
58#89733C2218yescomplemented
59#89731C2218yescomplemented
60#89724C2218yescomplemented
61#89721C2218yescomplemented
62#89720C2218yescomplemented
63#89448C2218yescomplemented
64#89447C2218yescomplemented
65#89432C2218yescomplemented
66#89431C2218yescomplemented
67C2×#2826—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C24×D7C2311yescharacteristic
71C22×C7×D4—24no—
72C22×C7×D4—42no—
73C22×C7×D4—42no—
74C22×C7×D4C2314yes—
75C23×C4×C7—42no—
76C23×C4×C7—42no—
77C23×C4×C7—42no—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2314yes—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7—42no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7C2314yes—
91C22×C22⋊D7C2314yes—
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C22⋊Dic7—24no—
106C2×C22⋊Dic7—42no—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7—42no—
109C2×C22⋊Dic7—42no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×(C2×D7)⋊C4—42no—
118C2×(C2×D7)⋊C4—42no—
119C2×(C2×D7)⋊C4—42no—
120C2×(C2×D7)⋊C4—42no—
121C2×(C2×D7)⋊C4—42no—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×C4⋊Dic7—42no—
128C2×C4⋊Dic7—42no—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×Dic7⋊C4—42no—
132C2×Dic7⋊C4—42no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4—42no—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C7×#95C2314yes—
142C7×#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151#2826—716no—
152C2×#400—71no—
153C2×#400—71no—
154C2×#399—71no—
155C2×#397—71no—
156C2×#397—71no—
157C2×#396—71no—
158C2×#396—71no—
159C2×#394—71no—
160C2×#394—71no—
161C2×#394—71no—
162C2×#394—71no—
163C2×#392—71no—
164C2×#386—71no—
165C2×#386D711yescharacteristic, complemented
166C2×#385—71no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7#4114yes—
181C24×C7C2412yes—
182C24×C7C2412yes—
183C24×C7C2411yescharacteristic
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7—22no—
191C23×D7C2412yes—
192C2×C7×D4—28no—
193C2×C7×D4—44no—
194C2×C7×D4—44no—
195C2×C7×D4—416no—
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—44no—
212C22×C4×C7—44no—
213C22×C4×C7—44no—
214C22×C4×C7—416no—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C2×C22⋊D7—28no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7—44no—
224C2×C22⋊D7—44no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7—416no—
227C2×C22⋊D7—416no—
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×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C7×C22⋊C4—44no—
257C7×C22⋊C4—44no—
258C7×C22⋊C4—44no—
259C22⋊Dic7—28no—
260C22⋊Dic7—44no—
261C22⋊Dic7—44no—
262C22⋊Dic7—44no—
263C22⋊Dic7—44no—
264C22⋊Dic7—44no—
265(C2×D7)⋊C4—44no—
266(C2×D7)⋊C4—44no—
267(C2×D7)⋊C4—44no—
268(C2×D7)⋊C4—44no—
269(C2×D7)⋊C4—44no—
270C4⋊Dic7—44no—
271C4⋊Dic7—44no—
272Dic7⋊C4—44no—
273Dic7⋊C4—44no—
274Dic7⋊C4—44no—
275Dic7⋊C4—44no—
276Dic7⋊C4—44no—
277C23×D4—71no—
278C23×D4—71no—
279C23×D4C2×D711yescharacteristic
280C24×C4C2×D711yescharacteristic
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302#400—78no—
303#400—78no—
304#399—78no—
305#397—78no—
306#397—78no—
307#396—78no—
308#396—78no—
309#394—78no—
310#394—78no—
311#394—78no—
312#394—78no—
313#392—78no—
314#386—78no—
315#386C2×D718yescomplemented
316#385—78no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7—28no—
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—44no—
344C23×C7—44no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7C2×#4114yes—
355C23×C7C2×#4112yes—
356C23×C7H(5,𝔽2)12yes—
357C23×C7H(5,𝔽2)12yes—
358C23×C7H(5,𝔽2)12yes—
359C23×C7H(5,𝔽2)12yes—
360C23×C7H(5,𝔽2)12yes—
361C23×C72−1+412yes—
362C23×C7C2511yescharacteristic
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—44no—
371C22×D7—44no—
372C22×D7—44no—
373C22×D7—44no—
374C22×D7—44no—
375C22×D7—44no—
376C22×D7—44no—
377C7×D4—416no—
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—416no—
394C2×C4×C7—44no—
395C2×C4×C7—44no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C2×C4×C7—44no—
399C22⋊D7—416no—
400C22⋊D7—416no—
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—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—22no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7—44no—
426C2×Dic7—44no—
427C2×Dic7—44no—
428C2×Dic7—44no—
429C25—71no—
430C25C22×D711yescharacteristic
431C25C22×D711yescharacteristic
432C22×D4—24no—
433C22×D4—42no—
434C22×D4—42no—
435C22×D4—74no—
436C22×D4—74no—
437C22×D4—144no—
438C22×D4—282no—
439C22×D4—282no—
440C22×D4—282no—
441C22×D4—282no—
442C22×D4—282no—
443C22×D4C22×D714yes—
444C23×C4—42no—
445C23×C4—42no—
446C23×C4—42no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4—71no—
451C23×C4—71no—
452C23×C4—71no—
453C23×C4—71no—
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D714yes—
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—74no—
467C2×C4⋊C4—282no—
468C2×C4⋊C4—282no—
469C2×C4⋊C4—282no—
470C2×C4⋊C4—282no—
471C2×C4⋊C4—282no—
472C2×C4⋊C4—282no—
473C2×C4⋊C4—282no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—74no—
478C2×C22⋊C4—74no—
479C2×C22⋊C4—74no—
480C2×C22⋊C4—74no—
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—282no—
490C2×C22⋊C4—282no—
491C2×C22⋊C4—282no—
492C2×C22⋊C4—282no—
493C2×C22⋊C4—282no—
494C2×C22⋊C4—282no—
495C2×C22⋊C4—282no—
496C2×C22⋊C4—282no—
497C2×C22⋊C4—282no—
498C2×C22⋊C4—282no—
499C2×C22⋊C4C22×D714yes—
500C2×C22⋊C4C22×D714yes—
501C2×C22⋊C4C22×D714yes—
502#95—74no—
503#95—74no—
504#95—74no—
505#95—74no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95—74no—
510#95C22×D714yes—
511#95C22×D714yes—
512C22×C7—24no—
513C22×C7—24no—
514C22×C7—24no—
515C22×C7—416no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—88no—
528C22×C7#53814yes—
529C22×C7#53814yes—
530C22×C7#53914yes—
531C22×C7#56014yes—
532C22×C7#56014yes—
533C22×C7#56214yes—
534C22×C7#56214yes—
535C22×C7C22×#4111yescharacteristic
536C22×C7C2×H(5,𝔽2)11yescharacteristic
537C22×C7C2×H(5,𝔽2)11yescharacteristic
538C22×C7C2×H(5,𝔽2)11yescharacteristic
539C22×C7C2×H(5,𝔽2)11yescharacteristic
540C22×C7C2×H(5,𝔽2)11yescharacteristic
541C22×C7C2×2−1+411yescharacteristic
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—88no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—72no—
576C24—142no—
577C24—142no—
578C24—142no—
579C24—142no—
580C24—142no—
581C24—142no—
582C24—142no—
583C24#115714yes—
584C24C23×D712yes—
585C24C23×D712yes—
586C24C23×D711yescharacteristic
587C2×D4—28no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—416no—
591C2×D4—148no—
592C2×D4—284no—
593C2×D4—284no—
594C2×D4—284no—
595C2×D4—284no—
596C2×D4—284no—
597C2×D4—2816no—
598C2×D4—2816no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—416no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—72no—
624C22×C4—72no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—142no—
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—142no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—142no—
643C22×C4—142no—
644C22×C4—142no—
645C22×C4—142no—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C22×C4C23×D712yes—
649C22×C4C23×D712yes—
650C22×C4C23×D712yes—
651C4⋊C4—284no—
652C4⋊C4—284no—
653C4⋊C4—284no—
654C4⋊C4—284no—
655C4⋊C4—284no—
656C4⋊C4—284no—
657C4⋊C4—284no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—148no—
662C22⋊C4—284no—
663C22⋊C4—284no—
664C22⋊C4—284no—
665C22⋊C4—284no—
666C22⋊C4—284no—
667C22⋊C4—284no—
668C22⋊C4—284no—
669C22⋊C4—284no—
670C22⋊C4—284no—
671C22⋊C4—284no—
672C2×C7—44no—
673C2×C7—82no—
674C2×C7#282618yescomplemented
675C2×C7C2×#53811yescharacteristic
676C2×C7C2×#53811yescharacteristic
677C2×C7C2×#53911yescharacteristic
678C2×C7C2×#56011yescharacteristic
679C2×C7C2×#56011yescharacteristic
680C2×C7C2×#56211yescharacteristic
681C2×C7C2×#56211yescharacteristic
682D7—82no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—142no—
711C23—142no—
712C23—142no—
713C23—142no—
714C23—142no—
715C23—142no—
716C23—142no—
717C23—284no—
718C23—284no—
719C23—284no—
720C23—284no—
721C23—284no—
722C23—284no—
723C23—284no—
724C23C2×#115714yes—
725C23C2×#115712yes—
726C23#654812yes—
727C23#654812yes—
728C23#654812yes—
729C23#654812yes—
730C23#655312yes—
731C23#655412yes—
732C23C24×D711yescharacteristic
733D4—416no—
734D4—2816no—
735D4—2816no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—416no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
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—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—284no—
779C2×C4—284no—
780C2×C4—284no—
781C2×C4—284no—
782C2×C4—284no—
783C2×C4—284no—
784C2×C4—284no—
785C7C2×#282611yescharacteristic, complemented, Sylow
786C22—24no—
787C22—24no—
788C22—24no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—416no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—88no—
802C22—282no—
803C22—282no—
804C22—282no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—282no—
809C22—568no—
810C22#9018514yes—
811C22#9025114yes—
812C22#9025514yes—
813C22#9028614yes—
814C22#9031114yes—
815C22#9031214yes—
816C22#9035814yes—
817C22C22×#115711yescharacteristic
818C22C2×#654811yescharacteristic
819C22C2×#654811yescharacteristic
820C22C2×#654811yescharacteristic
821C22C2×#654811yescharacteristic
822C22C2×#655311yescharacteristic
823C22C2×#655411yescharacteristic
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—282no—
830C4—282no—
831C4—282no—
832C4—282no—
833C4—282no—
834C4—282no—
835C4—282no—
836C2—44no—
837C2—82no—
838C2—562no—
839C2#1173231218yesdirect product factor
840C2C2×#9018511yescharacteristic
841C2C2×#9025511yescharacteristic
842C2C2×#9025111yescharacteristic
843C2C2×#9028611yescharacteristic
844C2C2×#9031111yescharacteristic
845C2C2×#9031211yescharacteristic
846C2C2×#9035811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#386D7
hypocenterC7C2×#2826
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×C7×#386C2semidirect
3. C2×#89994C2semidirect
4. C2×#89985C2semidirect
5. C2×#89982C2semidirect
6. C2×#89731C2semidirect
7. C2×#89721C2semidirect
8. C2×#89724C2semidirect
9. C2×#89720C2semidirect
10. C2×#89733C2semidirect
11. C2×#89733C2semidirect
12. #11732312C2direct (N × H)
13. C2×#89447C2semidirect
14. C2×#89448C2semidirect
15. C2×#89431C2semidirect
16. C2×#89432C2semidirect
42. C7×#386C22semidirect
46. #89994C22semidirect
47. #89985C22semidirect
48. #89982C22semidirect
57. #89733C22semidirect
58. #89733C22semidirect
59. #89731C22semidirect
60. #89724C22semidirect
61. #89721C22semidirect
62. #89720C22semidirect
63. #89448C22semidirect
64. #89447C22semidirect
65. #89432C22semidirect
66. #89431C22semidirect
165. C2×#386D7semidirect
315. #386C2×D7semidirect
674. C2×C7#2826semidirect
785. C7C2×#2826semidirect
839. C2#11732312direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3862
C2×#899952
C2×#899942
C2×#899852
C2×#899822
C2×#897312
C2×#897212
C2×#897242
C2×#897202
C2×#897332
#117323122
C2×#894472
C2×#894482
C2×#894312
C2×#894322
C2×#28267