Finite Group Databasebeta

← C2×#11731049 #13523925

Subgroups — C2×#11731049 #13523925

Order 1792.

3266 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×#6447C211yesmaximal, characteristic
2C22×#6442C211yesmaximal, characteristic, complemented
3C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C2×#89733C211yesmaximal, characteristic, complemented
7C2×#89733C211yesmaximal, characteristic, complemented
8C2×#89711C211yesmaximal, characteristic, complemented
9C2×#89700C211yesmaximal, characteristic, complemented
10C2×#89712C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
12#11731049C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89431C211yesmaximal, characteristic, complemented
15C2×#89444C211yesmaximal, characteristic, complemented
16C2×#89442C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6447—28no—
45C2×#6447C2218yes—
46C2×#6442—28no—
47C2×#6442C2218yescomplemented
48C4×C7×C22⋊C4C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51#89985C2218yescomplemented
52#89985C2218yescomplemented
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89733C2218yescomplemented
60#89733C2218yescomplemented
61#89712C2218yescomplemented
62#89711C2218yescomplemented
63C4×(C2×D7)⋊C4C2218yescomplemented
64#89700C2218yescomplemented
65#89444C2218yescomplemented
66#89442C2218yescomplemented
67#89440C2218yescomplemented
68#89431C2218yescomplemented
69C2×#2559—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—42no—
75C23×C4×C7—42no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2314yes—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7—42no—
89C22×C22⋊D7C2314yes—
90C22×C22⋊D7C2314yes—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C22×D28—24no—
98C22×D28—24no—
99C22×D28—42no—
100C22×D28C2314yes—
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—42no—
104C22×C4×D7C2314yes—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4D418yes—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C42×C7—42no—
110C2×C42×C7—42no—
111C2×C42×C7C2314yes—
112C2×C42×C7C2314yes—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×C4⋊Dic7—24no—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7—42no—
138C2×C4⋊Dic7C2314yes—
139C2×C4⋊Dic7C2314yes—
140C2×C4⋊Dic7C2314yes—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4—24no—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×C4×Dic7—24no—
148C2×C4×Dic7C2314yes—
149#6447—232no—
150#6442—232no—
151C7×#95C2314yes—
152C7×#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#121—71no—
161#2559—716no—
162C2×#400—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#394—71no—
166C2×#390—71no—
167C2×#389—71no—
168C2×#388—71no—
169C2×#388—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#385—71no—
173C2×C4×C22⋊C4—71no—
174C2×C4×C22⋊C4D711yescharacteristic, complemented
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7C2×D414yes—
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×D7—22no—
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7#4114yes—
198C23×D7C2412yes—
199C23×D7C2412yes—
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—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—28no—
215C22×C4×C7—44no—
216C22×C4×C7—44no—
217C22×C4×C7—416no—
218C22×C4×C7C2×D414yes—
219C22×C4×C7C2×D414yes—
220C22×C4×C7#4114yes—
221C22×C4×C7#4114yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C2×C22⋊D7—28no—
229C2×C22⋊D7—28no—
230C2×C22⋊D7—28no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—44no—
233C2×C22⋊D7—44no—
234C2×C22⋊D7—416no—
235C2×C22⋊D7—416no—
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—22no—
252C22×Dic7—22no—
253C22×Dic7#4114yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C2×D28—28no—
261C2×D28—28no—
262C2×D28—44no—
263C2×D28—416no—
264C2×C4×D7—28no—
265C2×C4×D7—28no—
266C2×C4×D7—44no—
267C2×C4×D7—416no—
268C7×C22⋊C4—28no—
269C7×C22⋊C4C2×D4116yes—
270C42×C7—44no—
271C42×C7—44no—
272C22⋊Dic7—28no—
273C22⋊Dic7—28no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4—28no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4—44no—
283C4⋊Dic7—28no—
284C4⋊Dic7—28no—
285C4⋊Dic7—44no—
286Dic7⋊C4—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—28no—
289C4×Dic7—28no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4—71no—
293C24×C4—71no—
294C24×C4C2×D711yescharacteristic
295C2×#126—78no—
296C2×#126—148no—
297C2×#121—78no—
298C2×#121—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×C22⋊C4—71no—
306C22×C22⋊C4—71no—
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×C42—71no—
319C22×C42C2×D711yescharacteristic
320C22×C42C2×D711yescharacteristic
321#400—78no—
322#394—78no—
323#394—78no—
324#394—78no—
325#390—78no—
326#389—78no—
327#388—78no—
328#388—78no—
329#386—78no—
330#386—78no—
331#385—78no—
332C4×C22⋊C4—78no—
333C4×C22⋊C4C2×D718yescomplemented
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95C2×D711yescharacteristic
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—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7—44no—
355C23×C7C22×D414yes—
356C23×C7C22×D412yes—
357C23×C7C2×#4112yes—
358C23×C7C2×#4112yes—
359C23×C7C2×#4112yes—
360C23×C7C2×#4112yes—
361C23×C7H(5,𝔽2)12yes—
362C23×C7H(5,𝔽2)12yes—
363C23×C7C2511yescharacteristic
364C22×D7—28no—
365C22×D7—28no—
366C22×D7—28no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—44no—
381C22×D7—44no—
382C22×D7—44no—
383C22×D7—44no—
384C22×D7—44no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7C2×#4114yes—
392C2×C4×C7—28no—
393C2×C4×C7—28no—
394C2×C4×C7—28no—
395C2×C4×C7—28no—
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—22no—
409C2×C4×C7—22no—
410C2×C4×C7—416no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C22×D414yes—
415C2×C4×C7C2×#4114yes—
416C2×C4×C7C2×#4114yes—
417C22⋊D7—416no—
418C22⋊D7—416no—
419C2×Dic7—28no—
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—22no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7C2×#4114yes—
443D28—416no—
444C4×D7—416no—
445C25—71no—
446C25—71no—
447C25C22×D711yescharacteristic
448C22×D4—74no—
449C22×D4—74no—
450C22×D4—74no—
451C22×D4—144no—
452C22×D4—144no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—144no—
457C22×D4—282no—
458C22×D4—282no—
459C22×D4—282no—
460C23×C4—24no—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—74no—
470C23×C4—144no—
471C23×C4—144no—
472C23×C4—282no—
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D714yes—
480#126—1432no—
481#121—1432no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4—282no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4D2818yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—42no—
521C2×C42—42no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42C22×D714yes—
525C2×C42C22×D714yes—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95C22×D714yes—
533#95C22×D714yes—
534C22×C7—24no—
535C22×C7—24no—
536C22×C7—24no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—416no—
542C22×C7#52914yes—
543C22×C7#53214yes—
544C22×C7#53814yes—
545C22×C7#54614yes—
546C22×C7#54614yes—
547C22×C7#55314yes—
548C22×C7#55314yes—
549C22×C7C23×D411yescharacteristic
550C22×C7C22×#4111yescharacteristic
551C22×C7C22×#4111yescharacteristic
552C22×C7C22×#4111yescharacteristic
553C22×C7C22×#4111yescharacteristic
554C22×C7C2×H(5,𝔽2)11yescharacteristic
555C22×C7C2×H(5,𝔽2)11yescharacteristic
556C2×D7—24no—
557C2×D7—24no—
558C2×D7—24no—
559C2×D7—42no—
560C2×D7—42no—
561C2×D7—42no—
562C2×D7—42no—
563C2×D7—416no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—88no—
572C4×C7—24no—
573C4×C7—24no—
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—42no—
577C4×C7—42no—
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—74no—
591C24—72no—
592C24—72no—
593C24—142no—
594C24—142no—
595C24—142no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24C2×D2814yes—
607C24C23×D712yes—
608C24C23×D711yescharacteristic
609C2×D4—148no—
610C2×D4—148no—
611C2×D4—148no—
612C2×D4—148no—
613C2×D4—148no—
614C2×D4—148no—
615C2×D4—284no—
616C2×D4—2816no—
617C2×D4—284no—
618C2×D4—284no—
619C2×D4—2816no—
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—28no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—416no—
639C22×C4—74no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—148no—
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—148no—
665C22×C4—284no—
666C22×C4—2816no—
667C22×C4C2×D2814yes—
668C22×C4C2×D2814yes—
669C22×C4#115714yes—
670C22×C4#115714yes—
671C22×C4C23×D712yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—148no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—148no—
682C4⋊C4—284no—
683C22⋊C4—28no—
684C22⋊C4—148no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—284no—
693C22⋊C4—284no—
694C22⋊C4—284no—
695C22⋊C4C2×D28116yes—
696C42—44no—
697C42—44no—
698C42—148no—
699C2×C7—44no—
700C2×C7#255918yescomplemented
701C2×C7C2×#52911yescharacteristic
702C2×C7C2×#53211yescharacteristic
703C2×C7C2×#53811yescharacteristic
704C2×C7C2×#54611yescharacteristic
705C2×C7C2×#54611yescharacteristic
706C2×C7C2×#55311yescharacteristic
707C2×C7C2×#55311yescharacteristic
708D7—44no—
709D7—82no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—74no—
724C23—148no—
725C23—148no—
726C23—148no—
727C23—142no—
728C23—142no—
729C23—142no—
730C23—142no—
731C23—142no—
732C23—142no—
733C23—142no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—284no—
741C23—284no—
742C23—284no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23—284no—
751C23C22×D2814yes—
752C23C22×D2812yes—
753C23C2×#115712yes—
754C23C2×#115712yes—
755C23#654812yes—
756C23#654812yes—
757C23D7×#4112yes—
758C23D7×#4112yes—
759C23C24×D711yescharacteristic
760D4—2816no—
761D4—2816no—
762D4—2816no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—74no—
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—2816no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4—284no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4C22×D2814yes—
810C2×C4C22×D2814yes—
811C2×C4C2×#115714yes—
812C2×C4C2×#115714yes—
813C7C2×#255911yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—416no—
820C22—42no—
821C22—42no—
822C22—144no—
823C22—144no—
824C22—144no—
825C22—282no—
826C22—282no—
827C22—2816no—
828C22—282no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—568no—
838C22#9016814yes—
839C22#9018514yes—
840C22#9021914yes—
841C22#9023114yes—
842C22#9024514yes—
843C22#9024514yes—
844C22#9024914yes—
845C22C23×D2811yescharacteristic
846C22C22×#115711yescharacteristic
847C22C22×#115711yescharacteristic
848C22C2×#654811yescharacteristic
849C22C2×#654811yescharacteristic
850C22C2×D7×#4111yescharacteristic
851C22C2×D7×#4111yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—144no—
859C4—282no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—284no—
866C2—562no—
867C2#1173104918yesdirect product factor
868C2C2×#9016811yescharacteristic
869C2C2×#9018511yescharacteristic
870C2C2×#9021911yescharacteristic
871C2C2×#9023111yescharacteristic
872C2C2×#9024511yescharacteristic
873C2C2×#9024511yescharacteristic
874C2C2×#9024911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC22×#6447C2
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2559
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#6442C2semidirect
3. C2×C4×C7×C22⋊C4C2semidirect
4. C2×#89985C2semidirect
5. C2×#89985C2semidirect
6. C2×#89733C2semidirect
7. C2×#89733C2semidirect
8. C2×#89711C2semidirect
9. C2×#89700C2semidirect
10. C2×#89712C2semidirect
11. C2×C4×(C2×D7)⋊C4C2semidirect
12. #11731049C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89431C2semidirect
15. C2×#89444C2semidirect
16. C2×#89442C2semidirect
47. C2×#6442C22semidirect
48. C4×C7×C22⋊C4C22semidirect
51. #89985C22semidirect
52. #89985C22semidirect
59. #89733C22semidirect
60. #89733C22semidirect
61. #89712C22semidirect
62. #89711C22semidirect
63. C4×(C2×D7)⋊C4C22semidirect
64. #89700C22semidirect
65. #89444C22semidirect
66. #89442C22semidirect
67. #89440C22semidirect
68. #89431C22semidirect
174. C2×C4×C22⋊C4D7semidirect
333. C4×C22⋊C4C2×D7semidirect
700. C2×C7#2559semidirect
813. C7C2×#2559semidirect
867. C2#11731049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64472
C22×#64422
C2×C4×C7×C22⋊C42
C2×#899852
C2×#897332
C2×#897112
C2×#897002
C2×#897122
C2×C4×(C2×D7)⋊C42
#117310492
C2×#894402
C2×#894312
C2×#894442
C2×#894422
C2×#25597