Finite Group Databasebeta

← C2×#11734419 #13520176

Subgroups — C2×#11734419 #13520176

Order 1792.

3218 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6446C211yesmaximal, characteristic, complemented
2C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic
5C2×#89992C211yesmaximal, characteristic, complemented
6C2×#89759C211yesmaximal, characteristic, complemented
7C2×#89755C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89720C211yesmaximal, characteristic, complemented
10C2×#89720C211yesmaximal, characteristic, complemented
11C2×#89733C211yesmaximal, characteristic, complemented
12C2×#89717C211yesmaximal, characteristic, complemented
13C2×#89722C211yesmaximal, characteristic, complemented
14#11734419C2116yesmaximal, direct product factor
15C2×#89447C211yesmaximal, characteristic, complemented
16C2×#89427C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6446—28no—
45C2×#6446C2218yescomplemented
46C2×(C22⋊D7)⋊C4—28no—
47C2×(C22⋊D7)⋊C4C2218yescomplemented
48C7×#394C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50#89995C2218yes—
51#89992C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89759C2218yescomplemented
60#89755C2218yescomplemented
61#89733C2218yescomplemented
62#89731C2218yescomplemented
63#89722C2218yescomplemented
64#89720C2218yescomplemented
65#89720C2218yescomplemented
66#89717C2218yescomplemented
67#89447C2218yescomplemented
68#89427C2218yescomplemented
69C2×#2630—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—42no—
75C22×C7×D4—42no—
76C22×C7×D4C2314yes—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7C2314yes—
89C22×C22⋊D7C2314yes—
90C23×Dic7—24no—
91C23×Dic7—42no—
92C23×Dic7—42no—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2314yes—
101C22×C4×D7—42no—
102C22×C4×D7—42no—
103C22×C4×D7D418yescomplemented
104C22×C4×D7C2314yes—
105C2×C7×C4⋊C4—42no—
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—42no—
118C2×C22⋊Dic7—42no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×(C2×D7)⋊C4—24no—
126C2×(C2×D7)⋊C4—24no—
127C2×(C2×D7)⋊C4—42no—
128C2×(C2×D7)⋊C4—42no—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×C4⋊Dic7—24no—
134C2×C4⋊Dic7—42no—
135C2×C4⋊Dic7—42no—
136C2×C4⋊Dic7C2314yes—
137C2×C4⋊Dic7C2314yes—
138C2×C4⋊Dic7C2314yes—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—42no—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×C4×Dic7—24no—
148C2×C4×Dic7C2314yes—
149#6446—232no—
150(C22⋊D7)⋊C4—232no—
151C7×#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#123—71no—
160C22×C4×D4—71no—
161#2630—716no—
162C2×#398—71no—
163C2×#397—71no—
164C2×#396—71no—
165C2×#396—71no—
166C2×#394—71no—
167C2×#394—71no—
168C2×#394D711yescharacteristic, complemented
169C2×#392—71no—
170C2×#388—71no—
171C2×#387—71no—
172C2×#386—71no—
173C2×#385—71no—
174C2×#380—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7#4114yes—
189C24×C7C2412yes—
190C24×C7C2412yes—
191C24×C7C2411yescharacteristic
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7—22no—
198C23×D7C2×D414yes—
199C23×D7C2412yes—
200C2×C7×D4—28no—
201C2×C7×D4—44no—
202C2×C7×D4—44no—
203C2×C7×D4—416no—
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—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7C2×D414yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C2×C22⋊D7—232no—
225C2×C22⋊D7—28no—
226C2×C22⋊D7—28no—
227C2×C22⋊D7—28no—
228C2×C22⋊D7—28no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—44no—
231C2×C22⋊D7—416no—
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×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—28no—
252C22×Dic7—44no—
253C22×Dic7—44no—
254C22×Dic7—416no—
255C22×Dic7C2×D414yes—
256C22×Dic7#4114yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C2×C4×D7—416no—
265C2×C4×D7—44no—
266C2×C4×D7—44no—
267C2×C4×D7C2×D4116yescomplemented
268C7×C4⋊C4—44no—
269C7×C22⋊C4—28no—
270C7×C22⋊C4—28no—
271C7×C22⋊C4—28no—
272C7×C22⋊C4—44no—
273C22⋊Dic7—28no—
274C22⋊Dic7—28no—
275C22⋊Dic7—44no—
276C22⋊Dic7—44no—
277C22⋊Dic7—44no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282C4⋊Dic7—28no—
283C4⋊Dic7—44no—
284C4⋊Dic7—44no—
285Dic7⋊C4—28no—
286Dic7⋊C4—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—44no—
289C4×Dic7—28no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4C2×D711yescharacteristic
293C24×C4—71no—
294C24×C4—71no—
295C2×#123—78no—
296C2×#123—148no—
297C2×C4×D4—78no—
298C2×C4×D4—148no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4C2×D711yescharacteristic
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C22⋊C4C2×D711yescharacteristic
320C22×C42—71no—
321#398—78no—
322#397—78no—
323#396—78no—
324#396—78no—
325#394—78no—
326#394—78no—
327#394C2×D718yescomplemented
328#392—78no—
329#388—78no—
330#387—78no—
331#386—78no—
332#385—78no—
333#380—78no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95C2×D711yescharacteristic
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—44no—
359C23×C7—44no—
360C23×C7—44no—
361C23×C7—44no—
362C23×C7—44no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7C22×D412yes—
370C23×C7C2×#4114yes—
371C23×C7C2×#4112yes—
372C23×C7C2×#4112yes—
373C23×C7H(5,𝔽2)12yes—
374C23×C7H(5,𝔽2)12yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C72−1+412yes—
377C23×C7C2511yescharacteristic
378C22×D7—28no—
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7C22×D414yes—
392C7×D4—416no—
393C2×C4×C7—28no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—44no—
409C2×C4×C7—44no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7C22×D414yes—
413C22⋊D7—232no—
414C22⋊D7—416no—
415C2×Dic7—28no—
416C2×Dic7—28no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—416no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7C22×D414yes—
443C2×Dic7C2×#4114yes—
444C4×D7—416no—
445C25—71no—
446C25C22×D711yescharacteristic
447C25C22×D711yescharacteristic
448C22×D4—24no—
449C22×D4—42no—
450C22×D4—42no—
451C22×D4—74no—
452C22×D4—74no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—282no—
458C22×D4—282no—
459C22×D4C22×D714yes—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—78no—
463C23×C4—74no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—74no—
470C23×C4—144no—
471C23×C4—282no—
472C23×C4—282no—
473C23×C4—282no—
474C23×C4—282no—
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#123—1432no—
481C4×D4—1432no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4—144no—
494C2×C4⋊C4—282no—
495C2×C4⋊C4—282no—
496C2×C4⋊C4—282no—
497C2×C4⋊C4C22×D714yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—74no—
509C2×C22⋊C4—74no—
510C2×C22⋊C4—74no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
518C2×C22⋊C4—282no—
519C2×C22⋊C4—282no—
520C2×C22⋊C4C22×D714yes—
521C2×C22⋊C4C22×D714yes—
522C2×C22⋊C4C22×D714yes—
523C2×C22⋊C4C22×D714yes—
524C2×C42—74no—
525C2×C42—144no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95C22×D714yes—
534C22×C7—24no—
535C22×C7—24no—
536C22×C7—24no—
537C22×C7—416no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—88no—
550C22×C7#52514yes—
551C22×C7#53414yes—
552C22×C7#53714yes—
553C22×C7#53814yes—
554C22×C7#53914yes—
555C22×C7#54014yes—
556C22×C7#54214yes—
557C22×C7C23×D411yescharacteristic
558C22×C7C22×#4111yescharacteristic
559C22×C7C22×#4111yescharacteristic
560C22×C7C2×H(5,𝔽2)11yescharacteristic
561C22×C7C2×H(5,𝔽2)11yescharacteristic
562C22×C7C2×H(5,𝔽2)11yescharacteristic
563C22×C7C2×2−1+411yescharacteristic
564C2×D7—24no—
565C2×D7—24no—
566C2×D7—24no—
567C2×D7—416no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C4×C7—24no—
573C4×C7—42no—
574C4×C7—42no—
575C4×C7—42no—
576C4×C7—42no—
577Dic7—24no—
578Dic7—24no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—74no—
598C24—72no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24#115914yes—
606C24C23×D712yes—
607C24C23×D712yes—
608C24C23×D711yescharacteristic
609C2×D4—28no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4—148no—
614C2×D4—148no—
615C2×D4—1432no—
616C2×D4—148no—
617C2×D4—148no—
618C2×D4—284no—
619C2×D4—284no—
620C2×D4—2816no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—74no—
636C22×C4—74no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—716no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—148no—
646C22×C4—142no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—2816no—
666C22×C4—284no—
667C22×C4—284no—
668C22×C4—284no—
669C22×C4—284no—
670C22×C4—2816no—
671C22×C4D4×D714yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—44no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—148no—
682C4⋊C4—284no—
683C4⋊C4—284no—
684C4⋊C4—284no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—44no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—284no—
694C22⋊C4—284no—
695C22⋊C4—284no—
696C22⋊C4—284no—
697C22⋊C4—284no—
698C42—148no—
699C2×C7—44no—
700C2×C7—82no—
701C2×C7#263018yescomplemented
702C2×C7C2×#52511yescharacteristic
703C2×C7C2×#53411yescharacteristic
704C2×C7C2×#53711yescharacteristic
705C2×C7C2×#53811yescharacteristic
706C2×C7C2×#53911yescharacteristic
707C2×C7C2×#54011yescharacteristic
708C2×C7C2×#54211yescharacteristic
709D7—44no—
710C23—28no—
711C23—28no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—74no—
738C23—148no—
739C23—148no—
740C23—148no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—142no—
745C23—142no—
746C23—142no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23C2×D4×D712yes—
752C23C2×#115914yes—
753C23C2×#115912yes—
754C23#654812yes—
755C23#654812yes—
756C23D7×#4112yes—
757C23#655312yes—
758C23#655412yes—
759C23C24×D711yescharacteristic
760D4—416no—
761D4—1432no—
762D4—2816no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—74no—
783C2×C4—74no—
784C2×C4—148no—
785C2×C4—148no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—2816no—
806C2×C4—2816no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4—284no—
810C2×C4—284no—
811C2×C4—284no—
812C2×C4C2×D4×D714yes—
813C7C2×#263011yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—416no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—144no—
831C22—144no—
832C22—144no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—2816no—
837C22—282no—
838C22#9028414yes—
839C22#9029614yes—
840C22#9029714yes—
841C22#9029914yes—
842C22#9035414yes—
843C22#9035614yes—
844C22#9036014yes—
845C22C22×D4×D711yescharacteristic
846C22C22×#115911yescharacteristic
847C22C2×#654811yescharacteristic
848C22C2×#654811yescharacteristic
849C22C2×D7×#4111yescharacteristic
850C22C2×#655311yescharacteristic
851C22C2×#655411yescharacteristic
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—144no—
858C4—144no—
859C4—282no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—82no—
866C2—284no—
867C2#1173441918yesdirect product factor
868C2C2×#9028411yescharacteristic
869C2C2×#9029711yescharacteristic
870C2C2×#9029611yescharacteristic
871C2C2×#9029911yescharacteristic
872C2C2×#9035611yescharacteristic
873C2C2×#9035411yescharacteristic
874C2C2×#9036011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#394D7
hypocenterC7C2×#2630
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#6446C2semidirect
2. C22×(C22⋊D7)⋊C4C2semidirect
3. C2×C7×#394C2semidirect
5. C2×#89992C2semidirect
6. C2×#89759C2semidirect
7. C2×#89755C2semidirect
8. C2×#89731C2semidirect
9. C2×#89720C2semidirect
10. C2×#89720C2semidirect
11. C2×#89733C2semidirect
12. C2×#89717C2semidirect
13. C2×#89722C2semidirect
14. #11734419C2direct (N × H)
15. C2×#89447C2semidirect
16. C2×#89427C2semidirect
45. C2×#6446C22semidirect
47. C2×(C22⋊D7)⋊C4C22semidirect
48. C7×#394C22semidirect
51. #89992C22semidirect
59. #89759C22semidirect
60. #89755C22semidirect
61. #89733C22semidirect
62. #89731C22semidirect
63. #89722C22semidirect
64. #89720C22semidirect
65. #89720C22semidirect
66. #89717C22semidirect
67. #89447C22semidirect
68. #89427C22semidirect
103. C22×C4×D7D4semidirect
168. C2×#394D7semidirect
267. C2×C4×D7C2×D4semidirect
327. #394C2×D7semidirect
701. C2×C7#2630semidirect
813. C7C2×#2630semidirect
867. C2#11734419direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64462
C22×(C22⋊D7)⋊C42
C2×C7×#3942
C2×#899952
C2×#899922
C2×#897592
C2×#897552
C2×#897312
C2×#897202
C2×#897332
C2×#897172
C2×#897222
#117344192
C2×#894472
C2×#894272
C2×#26307