Finite Group Databasebeta

← C2×#11734611 #13559999

Subgroups — C2×#11734611 #13559999

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×#394C211yesmaximal, characteristic, complemented
2C2×#89995C211yesmaximal, characteristic
3C2×#89994C211yesmaximal, characteristic, complemented
4C2×#89764C211yesmaximal, characteristic, complemented
5C2×#89758C211yesmaximal, characteristic, complemented
6C2×#89731C211yesmaximal, characteristic, complemented
7C2×#89728C211yesmaximal, characteristic, complemented
8C2×#89728C211yesmaximal, characteristic, complemented
9C2×#89725C211yesmaximal, characteristic, complemented
10C2×#89724C211yesmaximal, characteristic, complemented
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic, complemented
14#11734611C2116yesmaximal, direct product factor
15C2×#89440C211yesmaximal, characteristic, complemented
16C2×#89430C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C7×#394C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44#89995C2218yes—
45#89994C2218yescomplemented
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89764C2218yescomplemented
56#89758C2218yescomplemented
57#89733C2218yescomplemented
58#89731C2218yescomplemented
59#89728C2218yescomplemented
60#89728C2218yescomplemented
61#89725C2218yescomplemented
62#89724C2218yescomplemented
63#89720C2218yescomplemented
64#89720C2218yescomplemented
65#89440C2218yescomplemented
66#89430C2218yescomplemented
67C2×#2826—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C24×D7C2311yescharacteristic
71C22×C7×D4—42no—
72C22×C7×D4—42no—
73C22×C7×D4—42no—
74C22×C7×D4C2314yes—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—24no—
81C22×C22⋊D7—24no—
82C22×C22⋊D7—42no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7C2314yes—
87C22×C22⋊D7C2314yes—
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
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⋊C4—42no—
105C2×C7×C22⋊C4C2314yes—
106C2×C7×C22⋊C4C2314yes—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C22⋊Dic7—42no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7—42no—
113C2×C22⋊Dic7—42no—
114C2×C22⋊Dic7—42no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4—42no—
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⋊Dic7C2314yes—
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—
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×#394D711yescharacteristic, complemented
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×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
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#4114yes—
191C23×D7C2412yes—
192C2×C7×D4—44no—
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×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C2×C22⋊D7—28no—
217C2×C22⋊D7—28no—
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×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
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—
260C7×C22⋊C4—44no—
261C22⋊Dic7—44no—
262C22⋊Dic7—44no—
263C22⋊Dic7—44no—
264C22⋊Dic7—44no—
265C22⋊Dic7—44no—
266C22⋊Dic7—44no—
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—44no—
269(C2×D7)⋊C4—44no—
270(C2×D7)⋊C4—44no—
271C4⋊Dic7—44no—
272C4⋊Dic7—44no—
273Dic7⋊C4—44no—
274Dic7⋊C4—44no—
275Dic7⋊C4—44no—
276Dic7⋊C4—44no—
277C23×D4—71no—
278C23×D4—71no—
279C23×D4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
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#394C2×D718yescomplemented
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×#95—71no—
325C2×#95—71no—
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—22no—
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×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×C7—44no—
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—28no—
364C22×D7—28no—
365C22×D7—28no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—44no—
373C22×D7—44no—
374C22×D7—44no—
375C22×D7—44no—
376C22×D7C2×#4114yes—
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—44no—
394C2×C4×C7—44no—
395C2×C4×C7—44no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C22⋊D7—416no—
399C22⋊D7—416no—
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—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—
427C2×Dic7—44no—
428C4×D7—416no—
429C25—71no—
430C25C22×D711yescharacteristic
431C25C22×D711yescharacteristic
432C22×D4—42no—
433C22×D4—42no—
434C22×D4—42no—
435C22×D4—74no—
436C22×D4—74no—
437C22×D4—144no—
438C22×D4—144no—
439C22×D4—282no—
440C22×D4—282no—
441C22×D4—282no—
442C22×D4—282no—
443C22×D4C22×D714yes—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4—71no—
451C23×C4—74no—
452C23×C4—282no—
453C23×C4—282no—
454C23×C4—282no—
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—42no—
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⋊C4C22×D714yes—
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#95—74no—
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—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—88no—
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—24no—
543C2×D7—24no—
544C2×D7—24no—
545C2×D7—416no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—42no—
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—22no—
576C24—74no—
577C24—72no—
578C24—142no—
579C24—142no—
580C24—142no—
581C24—142no—
582C24—142no—
583C24—142no—
584C24C23×D712yes—
585C24C23×D712yes—
586C24C23×D711yescharacteristic
587C2×D4—44no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—416no—
591C2×D4—148no—
592C2×D4—148no—
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—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—142no—
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×C4—142no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—284no—
643C22×C4—284no—
644C22×C4—284no—
645C22×C4—2816no—
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—44no—
662C22⋊C4—148no—
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—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—44no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—74no—
712C23—148no—
713C23—148no—
714C23—148no—
715C23—142no—
716C23—142no—
717C23—142no—
718C23—142no—
719C23—142no—
720C23—142no—
721C23—284no—
722C23—284no—
723C23—284no—
724C23—284no—
725C23#654812yes—
726C23#654812yes—
727C23#654812yes—
728C23#654812yes—
729C23D7×#4112yes—
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—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
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—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—2816no—
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—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—88no—
801C22—88no—
802C22—144no—
803C22—144no—
804C22—144no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—2816no—
809C22—282no—
810C22#9028614yes—
811C22#9030414yes—
812C22#9031114yes—
813C22#9031214yes—
814C22#9035114yes—
815C22#9035814yes—
816C22#9036914yes—
817C22C2×#654811yescharacteristic
818C22C2×#654811yescharacteristic
819C22C2×#654811yescharacteristic
820C22C2×#654811yescharacteristic
821C22C2×D7×#4111yescharacteristic
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—82no—
837C2—82no—
838C2—284no—
839C2#1173461118yesdirect product factor
840C2C2×#9028611yescharacteristic
841C2C2×#9030411yescharacteristic
842C2C2×#9031111yescharacteristic
843C2C2×#9031211yescharacteristic
844C2C2×#9035111yescharacteristic
845C2C2×#9035811yescharacteristic
846C2C2×#9036911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#394D7
hypocenterC7C2×#2826
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×C7×#394C2semidirect
3. C2×#89994C2semidirect
4. C2×#89764C2semidirect
5. C2×#89758C2semidirect
6. C2×#89731C2semidirect
7. C2×#89728C2semidirect
8. C2×#89728C2semidirect
9. C2×#89725C2semidirect
10. C2×#89724C2semidirect
11. C2×#89720C2semidirect
12. C2×#89720C2semidirect
13. C2×#89733C2semidirect
14. #11734611C2direct (N × H)
15. C2×#89440C2semidirect
16. C2×#89430C2semidirect
42. C7×#394C22semidirect
45. #89994C22semidirect
55. #89764C22semidirect
56. #89758C22semidirect
57. #89733C22semidirect
58. #89731C22semidirect
59. #89728C22semidirect
60. #89728C22semidirect
61. #89725C22semidirect
62. #89724C22semidirect
63. #89720C22semidirect
64. #89720C22semidirect
65. #89440C22semidirect
66. #89430C22semidirect
162. C2×#394D7semidirect
312. #394C2×D7semidirect
674. C2×C7#2826semidirect
785. C7C2×#2826semidirect
839. C2#11734611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3942
C2×#899952
C2×#899942
C2×#897642
C2×#897582
C2×#897312
C2×#897282
C2×#897252
C2×#897242
C2×#897202
C2×#897332
#117346112
C2×#894402
C2×#894302
C2×#28267