Finite Group Databasebeta

← C2×#11735471 #13522367

Subgroups — C2×#11735471 #13522367

Order 1792.

3330 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×#6455C211yesmaximal, characteristic, complemented
2C22×#6449C211yesmaximal, characteristic, complemented
3C2×C7×#399C211yesmaximal, characteristic, complemented
4C2×#89765C211yesmaximal, characteristic, complemented
5C2×#89766C211yesmaximal, characteristic, complemented
6C2×#89760C211yesmaximal, characteristic, complemented
7C2×#89762C211yesmaximal, characteristic, complemented
8C2×#89753C211yesmaximal, characteristic, complemented
9C2×#89732C211yesmaximal, characteristic
10C2×#89728C211yesmaximal, characteristic, complemented
11C2×#89729C211yesmaximal, characteristic, complemented
12C2×#89730C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14#11735471C2116yesmaximal, direct product factor
15C2×#89437C211yesmaximal, characteristic, complemented
16C2×#89426C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6455—28no—
45C2×#6455C2218yescomplemented
46C2×#6449—28no—
47C2×#6449C2218yescomplemented
48C7×#399C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89766C2218yescomplemented
58#89765C2218yescomplemented
59#89762C2218yescomplemented
60#89760C2218yescomplemented
61#89753C2218yescomplemented
62#89732C2218yes—
63#89730C2218yescomplemented
64#89729C2218yescomplemented
65#89728C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67#89437C2218yescomplemented
68#89426C2218yescomplemented
69C2×#2471—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C22×C22⋊D7—24no—
80C22×C22⋊D7—24no—
81C22×C22⋊D7—24no—
82C22×C22⋊D7—24no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7C2314yes—
86C22×C22⋊D7C2314yes—
87C23×Dic7—24no—
88C23×Dic7—24no—
89C23×Dic7—42no—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2314yes—
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—24no—
104C22×C4×D7C2314yes—
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4—24no—
107C2×C7×C4⋊C4—42no—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C4⋊C4C2314yes—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—42no—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7C2314yes—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—24no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4—42no—
127C2×(C2×D7)⋊C4—42no—
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×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×C4⋊Dic7—24no—
138C2×C4⋊Dic7D418yescomplemented
139C2×C4⋊Dic7C2314yes—
140C2×C4⋊Dic7C2314yes—
141C2×Dic7⋊C4—42no—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7—24no—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149#6455—232no—
150#6449—232no—
151C7×#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#123—71no—
160C22×#117—71no—
161#2471—716no—
162C2×#399D711yescharacteristic, complemented
163C2×#397—71no—
164C2×#396—71no—
165C2×#392—71no—
166C2×#390—71no—
167C2×#390—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#387—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×#386—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7#4114yes—
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—22no—
215C22×C4×C7—22no—
216C22×C4×C7C2×D414yes—
217C22×C4×C7#4114yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C2×C22⋊D7—28no—
225C2×C22⋊D7—28no—
226C2×C22⋊D7—28no—
227C2×C22⋊D7—28no—
228C2×C22⋊D7—44no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—416no—
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—28no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—28no—
249C22×Dic7—44no—
250C22×Dic7—416no—
251C22×Dic7C2×D414yes—
252C22×Dic7C2×D414yes—
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—232no—
265C2×C4×D7—28no—
266C2×C4×D7—28no—
267C2×C4×D7—28no—
268C7×C4⋊C4—28no—
269C7×C4⋊C4—28no—
270C7×C4⋊C4—44no—
271C7×C22⋊C4—28no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—44no—
274C22⋊Dic7—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—
283(C2×D7)⋊C4—44no—
284C4⋊Dic7—28no—
285C4⋊Dic7C2×D4116yescomplemented
286Dic7⋊C4—44no—
287C4×Dic7—28no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4—71no—
293C24×C4—71no—
294C24×C4—71no—
295C2×#123—78no—
296C2×#123—148no—
297C2×#117—78no—
298C2×#117—148no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4C2×D711yescharacteristic
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C4⋊C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321#399C2×D718yescomplemented
322#397—78no—
323#396—78no—
324#392—78no—
325#390—78no—
326#390—78no—
327#388—78no—
328#387—78no—
329#387—78no—
330#386—78no—
331#386—78no—
332#386—78no—
333C4×C22⋊C4—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—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7—44no—
355C23×C7C22×D412yes—
356C23×C7C2×#4112yes—
357C23×C7C2×#4114yes—
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—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—22no—
409C2×C4×C7—22no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7—44no—
414C2×C4×C7C22×D414yes—
415C2×C4×C7C2×#4114yes—
416C22⋊D7—416no—
417C22⋊D7—416no—
418C2×Dic7—28no—
419C2×Dic7—28no—
420C2×Dic7—28no—
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×Dic7C22×D414yes—
441C2×Dic7C22×D414yes—
442C2×Dic7C2×#4114yes—
443D28—416no—
444C4×D7—232no—
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—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—74no—
467C23×C4—74no—
468C23×C4—144no—
469C23×C4—144no—
470C23×C4—144no—
471C23×C4—144no—
472C23×C4—144no—
473C23×C4—282no—
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#123—1432no—
481#117—1432no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—78no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—282no—
491C2×C4⋊C4C22×D714yes—
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
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—74no—
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—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—144no—
525C2×C42—282no—
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—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—416no—
542C22×C7#52514yes—
543C22×C7#52914yes—
544C22×C7#54014yes—
545C22×C7#54614yes—
546C22×C7#55014yes—
547C22×C7#55114yes—
548C22×C7#55114yes—
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—42no—
575C4×C7—42no—
576C4×C7—42no—
577C4×C7—42no—
578Dic7—24no—
579Dic7—24no—
580Dic7—24no—
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—
606C24#116114yes—
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—22no—
636C22×C4—22no—
637C22×C4—74no—
638C22×C4—74no—
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—148no—
648C22×C4—1432no—
649C22×C4—148no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—148no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—148no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—284no—
668C22×C4—2816no—
669C22×C4D4×D714yes—
670C22×C4#115914yes—
671C22×C4C23×D712yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—44no—
680C4⋊C4—716no—
681C4⋊C4—148no—
682C4⋊C4—284no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—44no—
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⋊C4—284no—
696C42—148no—
697C42—148no—
698C42—284no—
699C2×C7—44no—
700C2×C7#247118yescomplemented
701C2×C7C2×#52511yescharacteristic
702C2×C7C2×#52911yescharacteristic
703C2×C7C2×#54011yescharacteristic
704C2×C7C2×#54611yescharacteristic
705C2×C7C2×#55011yescharacteristic
706C2×C7C2×#55111yescharacteristic
707C2×C7C2×#55111yescharacteristic
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—
751C23C2×D4×D712yes—
752C23C2×#115912yes—
753C23#654812yes—
754C23C2×#116114yes—
755C23C2×#116112yes—
756C23D7×#4112yes—
757C23D7×#4112yes—
758C23#655312yes—
759C23C24×D711yescharacteristic
760D4—2816no—
761D4—2816no—
762D4—2816no—
763C2×C4—28no—
764C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—74no—
786C2×C4—74no—
787C2×C4—74no—
788C2×C4—1432no—
789C2×C4—148no—
790C2×C4—148no—
791C2×C4—148no—
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—142no—
806C2×C4—142no—
807C2×C4—2816no—
808C2×C4—284no—
809C2×C4—284no—
810C2×C4—284no—
811C2×C4C2×D4×D714yes—
812C2×C4C2×#115914yes—
813C7C2×#247111yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—144no—
823C22—144no—
824C22—144no—
825C22—282no—
826C22—282no—
827C22—282no—
828C22—282no—
829C22—2816no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—568no—
838C22#9031514yes—
839C22#9032114yes—
840C22#9032814yes—
841C22#9034714yes—
842C22#9034914yes—
843C22#9035414yes—
844C22#9040914yes—
845C22C22×D4×D711yescharacteristic
846C22C22×#115911yescharacteristic
847C22C2×#654811yescharacteristic
848C22C22×#116111yescharacteristic
849C22C2×D7×#4111yescharacteristic
850C22C2×D7×#4111yescharacteristic
851C22C2×#655311yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—144no—
859C4—144no—
860C4—144no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—284no—
866C2—562no—
867C2#1173547118yesdirect product factor
868C2C2×#9031511yescharacteristic
869C2C2×#9032111yescharacteristic
870C2C2×#9032811yescharacteristic
871C2C2×#9034711yescharacteristic
872C2C2×#9035411yescharacteristic
873C2C2×#9034911yescharacteristic
874C2C2×#9040911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#399C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×#399D7
hypocenterC7C2×#2471
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#6455C2semidirect
2. C22×#6449C2semidirect
3. C2×C7×#399C2semidirect
4. C2×#89765C2semidirect
5. C2×#89766C2semidirect
6. C2×#89760C2semidirect
7. C2×#89762C2semidirect
8. C2×#89753C2semidirect
10. C2×#89728C2semidirect
11. C2×#89729C2semidirect
12. C2×#89730C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. #11735471C2direct (N × H)
15. C2×#89437C2semidirect
16. C2×#89426C2semidirect
45. C2×#6455C22semidirect
47. C2×#6449C22semidirect
48. C7×#399C22semidirect
57. #89766C22semidirect
58. #89765C22semidirect
59. #89762C22semidirect
60. #89760C22semidirect
61. #89753C22semidirect
63. #89730C22semidirect
64. #89729C22semidirect
65. #89728C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. #89437C22semidirect
68. #89426C22semidirect
138. C2×C4⋊Dic7D4semidirect
162. C2×#399D7semidirect
285. C4⋊Dic7C2×D4semidirect
321. #399C2×D7semidirect
700. C2×C7#2471semidirect
813. C7C2×#2471semidirect
867. C2#11735471direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64552
C22×#64492
C2×C7×#3992
C2×#897652
C2×#897662
C2×#897602
C2×#897622
C2×#897532
C2×#897322
C2×#897282
C2×#897292
C2×#897302
C2×C22⋊C4×Dic72
#117354712
C2×#894372
C2×#894262
C2×#24717