Finite Group Databasebeta

← C2×#11735177 #13560004

Subgroups — C2×#11735177 #13560004

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×#397C211yesmaximal, characteristic, complemented
2C2×#89766C211yesmaximal, characteristic, complemented
3C2×#89761C211yesmaximal, characteristic, complemented
4C2×#89731C211yesmaximal, characteristic, complemented
5C2×#89732C211yesmaximal, characteristic
6C2×#89728C211yesmaximal, characteristic, complemented
7C2×#89720C211yesmaximal, characteristic, complemented
8C2×#89733C211yesmaximal, characteristic, complemented
9C2×#89733C211yesmaximal, characteristic, complemented
10#11735177C2116yesmaximal, direct product factor
11C2×#89449C211yesmaximal, characteristic, complemented
12C2×#89447C211yesmaximal, characteristic, complemented
13C2×#89437C211yesmaximal, characteristic, complemented
14C2×#89432C211yesmaximal, characteristic, complemented
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89444C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×D28C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C7×#397C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89766C2218yescomplemented
54#89761C2218yescomplemented
55#89733C2218yescomplemented
56#89733C2218yescomplemented
57#89732C2218yes—
58#89731C2218yescomplemented
59#89728C2218yescomplemented
60#89720C2218yescomplemented
61#89449C2218yescomplemented
62#89447C2218yescomplemented
63#89444C2218yescomplemented
64#89437C2218yescomplemented
65#89432C2218yescomplemented
66#89432C2218yescomplemented
67C2×#2826—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C24×D7C2311yescharacteristic
70C24×D7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C22×C22⋊D7—24no—
78C22×C22⋊D7—42no—
79C22×C22⋊D7—42no—
80C22×C22⋊D7—42no—
81C22×C22⋊D7—42no—
82C22×C22⋊D7—42no—
83C22×C22⋊D7C2314yes—
84C22×C22⋊D7C2314yes—
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C22×D28—24no—
92C22×D28—42no—
93C22×D28—42no—
94C22×D28C2314yes—
95C22×C4×D7—42no—
96C22×C4×D7—42no—
97C22×C4×D7—42no—
98C22×C4×D7C2314yes—
99C2×C7×C4⋊C4—42no—
100C2×C7×C4⋊C4C2314yes—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4—42no—
103C2×C7×C22⋊C4—42no—
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C7×C22⋊C4C2314yes—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7—42no—
109C2×C22⋊Dic7C2314yes—
110C2×C22⋊Dic7C2314yes—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—42no—
113C2×(C2×D7)⋊C4—42no—
114C2×(C2×D7)⋊C4—42no—
115C2×(C2×D7)⋊C4—42no—
116C2×(C2×D7)⋊C4—42no—
117C2×(C2×D7)⋊C4—42no—
118C2×(C2×D7)⋊C4—42no—
119C2×(C2×D7)⋊C4—42no—
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—42no—
130C2×C4⋊Dic7—42no—
131C2×C4⋊Dic7—42no—
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134C2×C4⋊Dic7C2314yes—
135C2×Dic7⋊C4—42no—
136C2×Dic7⋊C4—42no—
137C2×Dic7⋊C4—42no—
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×#397D711yescharacteristic, complemented
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×#386—71no—
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×C7C2412yes—
175C24×C7C2411yescharacteristic
176C23×D7—22no—
177C23×D7—22no—
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×D7#4114yes—
190C23×D7C2412yes—
191C23×D7C2412yes—
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×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C2×C22⋊D7—28no—
217C2×C22⋊D7—44no—
218C2×C22⋊D7—44no—
219C2×C22⋊D7—44no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7—416no—
223C2×C22⋊D7—416no—
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×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C2×D28—28no—
249C2×D28—44no—
250C2×D28—44no—
251C2×D28—416no—
252C2×C4×D7—44no—
253C2×C4×D7—44no—
254C2×C4×D7—44no—
255C2×C4×D7—416no—
256C7×C4⋊C4—44no—
257C7×C22⋊C4—44no—
258C7×C22⋊C4—44no—
259C7×C22⋊C4—44no—
260C22⋊Dic7—44no—
261C22⋊Dic7—44no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—44no—
264(C2×D7)⋊C4—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—
270(C2×D7)⋊C4—44no—
271C4⋊Dic7—44no—
272C4⋊Dic7—44no—
273C4⋊Dic7—44no—
274Dic7⋊C4—44no—
275Dic7⋊C4—44no—
276Dic7⋊C4—44no—
277C23×D4—71no—
278C23×D4—71no—
279C23×D4—71no—
280C24×C4—71no—
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⋊C4C2×D711yescharacteristic
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#397C2×D718yescomplemented
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#386—78no—
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×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7—44no—
337C23×C7—44no—
338C23×C7—44no—
339C23×C7—44no—
340C23×C7—44no—
341C23×C7C2×#4112yes—
342C23×C7H(5,𝔽2)12yes—
343C23×C7H(5,𝔽2)12yes—
344C23×C7H(5,𝔽2)12yes—
345C23×C7H(5,𝔽2)12yes—
346C23×C7H(5,𝔽2)12yes—
347C23×C72−1+412yes—
348C23×C7C2511yescharacteristic
349C22×D7—28no—
350C22×D7—28no—
351C22×D7—28no—
352C22×D7—22no—
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—22no—
365C22×D7—44no—
366C22×D7—44no—
367C22×D7—44no—
368C22×D7—44no—
369C22×D7—44no—
370C22×D7—44no—
371C22×D7—44no—
372C22×D7—44no—
373C22×D7—44no—
374C22×D7—44no—
375C22×D7—44no—
376C22×D7C2×#4114yes—
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—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—44no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C2×C4×C7—44no—
399C2×C4×C7—44no—
400C2×C4×C7—44no—
401C22⋊D7—416no—
402C22⋊D7—416no—
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—44no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7—44no—
426C2×Dic7—44no—
427D28—416no—
428C4×D7—416no—
429C25—71no—
430C25—71no—
431C25C22×D711yescharacteristic
432C22×D4—74no—
433C22×D4—74no—
434C22×D4—74no—
435C22×D4—144no—
436C22×D4—144no—
437C22×D4—282no—
438C22×D4—282no—
439C22×D4—282no—
440C22×D4—282no—
441C22×D4—282no—
442C22×D4—282no—
443C22×D4—282no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4—74no—
451C23×C4—282no—
452C23×C4—282no—
453C23×C4—282no—
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C2×C4⋊C4—42no—
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⋊C4C22×D714yes—
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#95C22×D714yes—
510#95C22×D714yes—
511#95C22×D714yes—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—88no—
520C22×C7#53814yes—
521C22×C7#53814yes—
522C22×C7#53914yes—
523C22×C7#56014yes—
524C22×C7#56014yes—
525C22×C7#56214yes—
526C22×C7#56214yes—
527C22×C7C22×#4111yescharacteristic
528C22×C7C2×H(5,𝔽2)11yescharacteristic
529C22×C7C2×H(5,𝔽2)11yescharacteristic
530C22×C7C2×H(5,𝔽2)11yescharacteristic
531C22×C7C2×H(5,𝔽2)11yescharacteristic
532C22×C7C2×H(5,𝔽2)11yescharacteristic
533C22×C7C2×2−1+411yescharacteristic
534C2×D7—24no—
535C2×D7—24no—
536C2×D7—24no—
537C2×D7—416no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—42no—
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—
555C4×C7—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—74no—
570C24—72no—
571C24—72no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24—142no—
576C24—142no—
577C24—142no—
578C24—142no—
579C24—142no—
580C24—142no—
581C24—142no—
582C24—142no—
583C24—142no—
584C24—142no—
585C24C23×D712yes—
586C24C23×D711yescharacteristic
587C2×D4—148no—
588C2×D4—148no—
589C2×D4—284no—
590C2×D4—284no—
591C2×D4—2816no—
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—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—142no—
624C22×C4—142no—
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—284no—
642C22×C4—284no—
643C22×C4—284no—
644C22×C4—2816no—
645C22×C4C23×D712yes—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C22×C4C23×D712yes—
649C22×C4C23×D712yes—
650C22×C4C23×D712yes—
651C4⋊C4—44no—
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—82no—
673C2×C7#282618yescomplemented
674C2×C7C2×#53811yescharacteristic
675C2×C7C2×#53811yescharacteristic
676C2×C7C2×#53911yescharacteristic
677C2×C7C2×#56011yescharacteristic
678C2×C7C2×#56011yescharacteristic
679C2×C7C2×#56211yescharacteristic
680C2×C7C2×#56211yescharacteristic
681D7—44no—
682D7—82no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—74no—
698C23—148no—
699C23—148no—
700C23—148no—
701C23—142no—
702C23—142no—
703C23—142no—
704C23—142no—
705C23—142no—
706C23—142no—
707C23—142no—
708C23—142no—
709C23—142no—
710C23—142no—
711C23—142no—
712C23—142no—
713C23—142no—
714C23—284no—
715C23—284no—
716C23—284no—
717C23—284no—
718C23—284no—
719C23—284no—
720C23—284no—
721C23—284no—
722C23—284no—
723C23—284no—
724C23—284no—
725C23#654812yes—
726C23#654812yes—
727C23D7×#4112yes—
728C23#655312yes—
729C23#655312yes—
730C23#655312yes—
731C23#655412yes—
732C23C24×D711yescharacteristic
733D4—2816no—
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—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
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—2816no—
779C2×C4—284no—
780C2×C4—284no—
781C2×C4—284no—
782C2×C4—284no—
783C2×C4—284no—
784C2×C4—284no—
785C7C2×#282611yescharacteristic, complemented, Sylow
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—88no—
794C22—144no—
795C22—144no—
796C22—144no—
797C22—282no—
798C22—282no—
799C22—2816no—
800C22—282no—
801C22—282no—
802C22—282no—
803C22—282no—
804C22—282no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—282no—
809C22—568no—
810C22#9031114yes—
811C22#9034814yes—
812C22#9034814yes—
813C22#9035814yes—
814C22#9037514yes—
815C22#9039814yes—
816C22#9040214yes—
817C22C2×#654811yescharacteristic
818C22C2×#654811yescharacteristic
819C22C2×D7×#4111yescharacteristic
820C22C2×#655311yescharacteristic
821C22C2×#655311yescharacteristic
822C22C2×#655311yescharacteristic
823C22C2×#655411yescharacteristic
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—282no—
831C4—282no—
832C4—282no—
833C4—282no—
834C4—282no—
835C4—282no—
836C2—82no—
837C2—284no—
838C2—562no—
839C2#1173517718yesdirect product factor
840C2C2×#9031111yescharacteristic
841C2C2×#9034811yescharacteristic
842C2C2×#9034811yescharacteristic
843C2C2×#9035811yescharacteristic
844C2C2×#9037511yescharacteristic
845C2C2×#9039811yescharacteristic
846C2C2×#9040211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#397C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×#397D7
hypocenterC7C2×#2826
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C7×#397C2semidirect
2. C2×#89766C2semidirect
3. C2×#89761C2semidirect
4. C2×#89731C2semidirect
6. C2×#89728C2semidirect
7. C2×#89720C2semidirect
8. C2×#89733C2semidirect
9. C2×#89733C2semidirect
10. #11735177C2direct (N × H)
11. C2×#89449C2semidirect
12. C2×#89447C2semidirect
13. C2×#89437C2semidirect
14. C2×#89432C2semidirect
15. C2×#89432C2semidirect
16. C2×#89444C2semidirect
42. C7×#397C22semidirect
53. #89766C22semidirect
54. #89761C22semidirect
55. #89733C22semidirect
56. #89733C22semidirect
58. #89731C22semidirect
59. #89728C22semidirect
60. #89720C22semidirect
61. #89449C22semidirect
62. #89447C22semidirect
63. #89444C22semidirect
64. #89437C22semidirect
65. #89432C22semidirect
66. #89432C22semidirect
156. C2×#397D7semidirect
306. #397C2×D7semidirect
673. C2×C7#2826semidirect
785. C7C2×#2826semidirect
839. C2#11735177direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3972
C2×#897662
C2×#897612
C2×#897312
C2×#897322
C2×#897282
C2×#897202
C2×#897332
#117351772
C2×#894492
C2×#894472
C2×#894372
C2×#894322
C2×#894442
C2×#28267