Finite Group Databasebeta

← C2×#11734848 #13560122

Subgroups — C2×#11734848 #13560122

Order 1792.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic, complemented
2C2×#89764C211yesmaximal, characteristic, complemented
3C2×#89765C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89763C211yesmaximal, characteristic, complemented
6C2×#89752C211yesmaximal, characteristic, complemented
7C2×#89762C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89731C211yesmaximal, characteristic, complemented
10C2×#89732C211yesmaximal, characteristic
11C2×#89724C211yesmaximal, characteristic, complemented
12C2×#89733C211yesmaximal, characteristic, complemented
13C2×#89729C211yesmaximal, characteristic, complemented
14#11734848C2116yesmaximal, direct product factor
15C2×#89444C211yesmaximal, characteristic, complemented
16C2×#89425C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×D28C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C7×#396C2218yescomplemented
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#89765C2218yescomplemented
55#89764C2218yescomplemented
56#89763C2218yescomplemented
57#89762C2218yescomplemented
58#89752C2218yescomplemented
59#89733C2218yescomplemented
60#89732C2218yes—
61#89731C2218yescomplemented
62#89731C2218yescomplemented
63#89729C2218yescomplemented
64#89724C2218yescomplemented
65#89444C2218yescomplemented
66#89425C2218yescomplemented
67C2×#2829—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—42no—
92C22×D28—42no—
93C22×D28—42no—
94C22×D28C2314yes—
95C2×C7×C4⋊C4—42no—
96C2×C7×C4⋊C4—42no—
97C2×C7×C4⋊C4—42no—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C4⋊C4C2314yes—
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)⋊C4—42no—
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×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×C4⋊Dic7—24no—
132C2×C4⋊Dic7C2314yes—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4—42no—
136C2×Dic7⋊C4—42no—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×C4×Dic7—42no—
142C2×C4×Dic7C2314yes—
143C7×#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151#2829—716no—
152C2×#399—71no—
153C2×#398—71no—
154C2×#397—71no—
155C2×#397—71no—
156C2×#396—71no—
157C2×#396D711yescharacteristic, complemented
158C2×#394—71no—
159C2×#394—71no—
160C2×#394—71no—
161C2×#394—71no—
162C2×#394—71no—
163C2×#392—71no—
164C2×#390—71no—
165C2×#388—71no—
166C2×#387—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—22no—
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#4114yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C2×D28—44no—
249C2×D28—44no—
250C2×D28—44no—
251C2×D28—416no—
252C7×C4⋊C4—44no—
253C7×C4⋊C4—44no—
254C7×C4⋊C4—44no—
255C7×C22⋊C4—44no—
256C7×C22⋊C4—44no—
257C7×C22⋊C4—44no—
258C22⋊Dic7—44no—
259C22⋊Dic7—44no—
260(C2×D7)⋊C4—28no—
261(C2×D7)⋊C4—44no—
262(C2×D7)⋊C4—44no—
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—
270C4⋊Dic7—28no—
271Dic7⋊C4—44no—
272Dic7⋊C4—44no—
273Dic7⋊C4—44no—
274Dic7⋊C4—44no—
275C4×Dic7—44no—
276C23×D4—71no—
277C23×D4—71no—
278C23×D4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C4⋊C4C2×D711yescharacteristic
286C22×C4⋊C4C2×D711yescharacteristic
287C22×C22⋊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
302C22×C42—71no—
303#399—78no—
304#398—78no—
305#397—78no—
306#397—78no—
307#396—78no—
308#396C2×D718yescomplemented
309#394—78no—
310#394—78no—
311#394—78no—
312#394—78no—
313#394—78no—
314#392—78no—
315#390—78no—
316#388—78no—
317#387—78no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95C2×D711yescharacteristic
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7—44no—
337C23×C7—44no—
338C23×C7—44no—
339C23×C7—44no—
340C23×C7C2×#4112yes—
341C23×C7H(5,𝔽2)12yes—
342C23×C7H(5,𝔽2)12yes—
343C23×C7H(5,𝔽2)12yes—
344C23×C7H(5,𝔽2)12yes—
345C23×C7H(5,𝔽2)12yes—
346C23×C72−1+412yes—
347C23×C7C2511yescharacteristic
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
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—44no—
363C22×D7—44no—
364C22×D7—44no—
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—
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—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—44no—
395C2×C4×C7—44no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C2×C4×C7—44no—
399C2×C4×C7—44no—
400C22⋊D7—416no—
401C22⋊D7—416no—
402C2×Dic7—28no—
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—44no—
421C2×Dic7—44no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7C2×#4114yes—
426D28—416no—
427C25—71no—
428C25—71no—
429C25C22×D711yescharacteristic
430C22×D4—74no—
431C22×D4—74no—
432C22×D4—74no—
433C22×D4—144no—
434C22×D4—282no—
435C22×D4—282no—
436C22×D4—282no—
437C22×D4—282no—
438C22×D4—282no—
439C22×D4—282no—
440C22×D4—282no—
441C22×D4—282no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4C22×D711yescharacteristic
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—282no—
464C2×C4⋊C4—282no—
465C2×C4⋊C4—282no—
466C2×C4⋊C4—282no—
467C2×C4⋊C4C22×D714yes—
468C2×C4⋊C4C22×D714yes—
469C2×C4⋊C4C22×D714yes—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—74no—
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—144no—
486C2×C22⋊C4—282no—
487C2×C22⋊C4—282no—
488C2×C22⋊C4—282no—
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⋊C4C22×D714yes—
498C2×C22⋊C4C22×D714yes—
499C2×C22⋊C4C22×D714yes—
500C2×C42—74no—
501C2×C42—282no—
502#95—74no—
503#95—74no—
504#95—74no—
505#95—74no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95C22×D714yes—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7—88no—
518C22×C7#53814yes—
519C22×C7#54014yes—
520C22×C7#54214yes—
521C22×C7#56014yes—
522C22×C7#56014yes—
523C22×C7#56214yes—
524C22×C7#56214yes—
525C22×C7C22×#4111yescharacteristic
526C22×C7C2×H(5,𝔽2)11yescharacteristic
527C22×C7C2×H(5,𝔽2)11yescharacteristic
528C22×C7C2×H(5,𝔽2)11yescharacteristic
529C22×C7C2×H(5,𝔽2)11yescharacteristic
530C22×C7C2×H(5,𝔽2)11yescharacteristic
531C22×C7C2×2−1+411yescharacteristic
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
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—88no—
547C2×D7—88no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554Dic7—24no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—72no—
568C24—72no—
569C24—142no—
570C24—142no—
571C24—142no—
572C24—142no—
573C24—142no—
574C24—142no—
575C24—142no—
576C24—142no—
577C24—142no—
578C24—142no—
579C24—142no—
580C24—142no—
581C24—142no—
582C24—142no—
583C24C23×D712yes—
584C24C23×D711yescharacteristic
585C2×D4—148no—
586C2×D4—284no—
587C2×D4—284no—
588C2×D4—284no—
589C2×D4—2816no—
590C2×D4—284no—
591C2×D4—284no—
592C2×D4—284no—
593C2×D4—284no—
594C2×D4—284no—
595C2×D4—2816no—
596C2×D4—2816no—
597C22×C4—22no—
598C22×C4—22no—
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—74no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—72no—
622C22×C4—142no—
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×C4C23×D712yes—
640C22×C4C23×D712yes—
641C22×C4C23×D712yes—
642C22×C4C23×D712yes—
643C22×C4C23×D712yes—
644C22×C4C23×D712yes—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—148no—
649C4⋊C4—284no—
650C4⋊C4—284no—
651C4⋊C4—284no—
652C4⋊C4—284no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—148no—
657C22⋊C4—284no—
658C22⋊C4—284no—
659C22⋊C4—284no—
660C22⋊C4—284no—
661C22⋊C4—284no—
662C22⋊C4—284no—
663C22⋊C4—284no—
664C22⋊C4—284no—
665C22⋊C4—284no—
666C22⋊C4—284no—
667C22⋊C4—284no—
668C42—284no—
669C2×C7—82no—
670C2×C7#282918yescomplemented
671C2×C7C2×#53811yescharacteristic
672C2×C7C2×#54011yescharacteristic
673C2×C7C2×#54211yescharacteristic
674C2×C7C2×#56011yescharacteristic
675C2×C7C2×#56011yescharacteristic
676C2×C7C2×#56211yescharacteristic
677C2×C7C2×#56211yescharacteristic
678D7—82no—
679D7—82no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—142no—
695C23—142no—
696C23—142no—
697C23—142no—
698C23—142no—
699C23—142no—
700C23—142no—
701C23—142no—
702C23—142no—
703C23—142no—
704C23—142no—
705C23—142no—
706C23—142no—
707C23—142no—
708C23—284no—
709C23—284no—
710C23—284no—
711C23—284no—
712C23—284no—
713C23—284no—
714C23—284no—
715C23—284no—
716C23—284no—
717C23—284no—
718C23—284no—
719C23—284no—
720C23—284no—
721C23—284no—
722C23#654812yes—
723C23#654812yes—
724C23#654812yes—
725C23#655112yes—
726C23D7×#4112yes—
727C23#655312yes—
728C23#655312yes—
729C23C24×D711yescharacteristic
730D4—2816no—
731D4—2816no—
732D4—2816no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
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—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—74no—
758C2×C4—148no—
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—284no—
777C2×C4—284no—
778C2×C4—284no—
779C2×C4—284no—
780C2×C4—284no—
781C7C2×#282911yescharacteristic, complemented, Sylow
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—88no—
790C22—282no—
791C22—282no—
792C22—282no—
793C22—282no—
794C22—282no—
795C22—282no—
796C22—282no—
797C22—282no—
798C22—282no—
799C22—282no—
800C22—282no—
801C22—282no—
802C22—282no—
803C22—282no—
804C22—568no—
805C22—568no—
806C22#9030614yes—
807C22#9031114yes—
808C22#9031114yes—
809C22#9033114yes—
810C22#9033814yes—
811C22#9033814yes—
812C22#9039514yes—
813C22C2×#654811yescharacteristic
814C22C2×#654811yescharacteristic
815C22C2×#654811yescharacteristic
816C22C2×#655111yescharacteristic
817C22C2×D7×#4111yescharacteristic
818C22C2×#655311yescharacteristic
819C22C2×#655311yescharacteristic
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—144no—
827C4—282no—
828C4—282no—
829C4—282no—
830C4—282no—
831C4—282no—
832C2—82no—
833C2—562no—
834C2—562no—
835C2#1173484818yesdirect product factor
836C2C2×#9030611yescharacteristic
837C2C2×#9031111yescharacteristic
838C2C2×#9031111yescharacteristic
839C2C2×#9033111yescharacteristic
840C2C2×#9033811yescharacteristic
841C2C2×#9033811yescharacteristic
842C2C2×#9039511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×#396D7
hypocenterC7C2×#2829
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C2×C7×#396C2semidirect
2. C2×#89764C2semidirect
3. C2×#89765C2semidirect
4. C2×#89766C2semidirect
5. C2×#89763C2semidirect
6. C2×#89752C2semidirect
7. C2×#89762C2semidirect
8. C2×#89731C2semidirect
9. C2×#89731C2semidirect
11. C2×#89724C2semidirect
12. C2×#89733C2semidirect
13. C2×#89729C2semidirect
14. #11734848C2direct (N × H)
15. C2×#89444C2semidirect
16. C2×#89425C2semidirect
44. C7×#396C22semidirect
53. #89766C22semidirect
54. #89765C22semidirect
55. #89764C22semidirect
56. #89763C22semidirect
57. #89762C22semidirect
58. #89752C22semidirect
59. #89733C22semidirect
61. #89731C22semidirect
62. #89731C22semidirect
63. #89729C22semidirect
64. #89724C22semidirect
65. #89444C22semidirect
66. #89425C22semidirect
157. C2×#396D7semidirect
308. #396C2×D7semidirect
670. C2×C7#2829semidirect
781. C7C2×#2829semidirect
835. C2#11734848direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×#897642
C2×#897652
C2×#897662
C2×#897632
C2×#897522
C2×#897622
C2×#897312
C2×#897322
C2×#897242
C2×#897332
C2×#897292
#117348482
C2×#894442
C2×#894252
C2×#28297