Finite Group Databasebeta

← C2×#11739724 #13522366

Subgroups — C2×#11739724 #13522366

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×C7×#117C211yesmaximal, characteristic, complemented
2C22×#6457C211yesmaximal, characteristic, complemented
3C2×#89985C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5#11739724C2116yesmaximal, direct product factor
6C2×#89764C211yesmaximal, characteristic, complemented
7C2×#89765C211yesmaximal, characteristic, complemented
8C2×#89753C211yesmaximal, characteristic, complemented
9C2×#89732C211yesmaximal, characteristic
10C2×#89728C211yesmaximal, characteristic, complemented
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89729C211yesmaximal, characteristic, complemented
13C2×#89711C211yesmaximal, characteristic, complemented
14C2×#89712C211yesmaximal, characteristic, complemented
15C2×#89705C211yesmaximal, characteristic, complemented
16C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C2×C7×#117—28no—
23C2×C7×#117C2218yescomplemented
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×C4⋊Dic7C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6457—28no—
47C2×#6457C2218yescomplemented
48#89985C2218yescomplemented
49#89985C2218yescomplemented
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89765C2218yescomplemented
59#89764C2218yescomplemented
60#89753C2218yescomplemented
61#89732C2218yes—
62#89729C2218yescomplemented
63#89728C2218yescomplemented
64#89720C2218yescomplemented
65#89712C2218yescomplemented
66#89711C2218yescomplemented
67C4×(C2×D7)⋊C4C2218yescomplemented
68#89705C2218yescomplemented
69C2×#2471—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7—24no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2314yes—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
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—
105C7×#117—232no—
106C2×C7×C4⋊C4—24no—
107C2×C7×C4⋊C4D418yescomplemented
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C4⋊C4C2314yes—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4C2314yes—
113C2×C7×C22⋊C4C2314yes—
114C2×C42×C7—24no—
115C2×C42×C7—24no—
116C2×C42×C7C2314yes—
117C2×C42×C7C2314yes—
118C2×C22⋊Dic7—42no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—24no—
124C2×(C2×D7)⋊C4—24no—
125C2×(C2×D7)⋊C4—24no—
126C2×(C2×D7)⋊C4—24no—
127C2×(C2×D7)⋊C4—24no—
128C2×(C2×D7)⋊C4—42no—
129C2×(C2×D7)⋊C4—42no—
130C2×(C2×D7)⋊C4—42no—
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×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×C4⋊Dic7—42no—
141C2×C4⋊Dic7C2314yes—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4—24no—
144C2×Dic7⋊C4—42no—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×Dic7⋊C4C2314yes—
148C2×C4×Dic7—42no—
149C2×C4×Dic7C2314yes—
150#6457—232no—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#123—71no—
160C22×#117D711yescharacteristic, complemented
161#2471—716no—
162C2×#399—71no—
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—232no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—28no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—28no—
211C22×C4×C7—28no—
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×C7C2×D414yes—
220C22×C4×C7C2×D414yes—
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×C4⋊C4—28no—
269C7×C4⋊C4C2×D4116yescomplemented
270C7×C22⋊C4—28no—
271C7×C22⋊C4—28no—
272C42×C7—28no—
273C42×C7—28no—
274C22⋊Dic7—44no—
275C22⋊Dic7—44no—
276(C2×D7)⋊C4—28no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—44no—
283(C2×D7)⋊C4—44no—
284(C2×D7)⋊C4—44no—
285C4⋊Dic7—44no—
286Dic7⋊C4—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—44no—
289C4×Dic7—44no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4—71no—
293C24×C4—71no—
294C24×C4C2×D711yescharacteristic
295C2×#123—78no—
296C2×#123—148no—
297C2×#117—28no—
298C2×#117C2×D718yescomplemented
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
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⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320C22×C42C2×D711yescharacteristic
321#399—78no—
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×#95—71no—
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×#4114yes—
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—232no—
393C2×C4×C7—28no—
394C2×C4×C7—28no—
395C2×C4×C7—28no—
396C2×C4×C7—28no—
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—22no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C22×D414yes—
415C2×C4×C7C22×D414yes—
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—24no—
462C23×C4—24no—
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×D714yes—
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#123—1432no—
481#117—232no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—144no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4—282no—
490C2×C4⋊C4—282no—
491C2×C4⋊C4C22⋊D718yescomplemented
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
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—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⋊C4—282no—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—24no—
521C2×C42—24no—
522C2×C42—74no—
523C2×C42—282no—
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#95—74no—
533#95—74no—
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—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—
606C24#115714yes—
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—232no—
622C22×C4—28no—
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—28no—
632C22×C4—28no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
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×C4#115714yes—
668C22×C4C2×C22⋊D714yes—
669C22×C4C2×C22⋊D714yes—
670C22×C4C2×C22⋊D714yes—
671C22×C4C23×D712yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—28no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—284no—
681C4⋊C4—284no—
682C4⋊C4C2×C22⋊D7116yescomplemented
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—284no—
692C22⋊C4—284no—
693C22⋊C4—284no—
694C22⋊C4—284no—
695C22⋊C4—284no—
696C42—28no—
697C42—28no—
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×#115714yes—
752C23C2×#115712yes—
753C23C2×#115712yes—
754C23D7×#4112yes—
755C23D7×#4112yes—
756C23#655312yes—
757C23#655312yes—
758C23C22×C22⋊D712yes—
759C23C24×D711yescharacteristic
760D4—2816no—
761D4—2816no—
762D4—2816no—
763C2×C4—232no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
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—22no—
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×C4C2×#115714yes—
810C2×C4C22×C22⋊D714yes—
811C2×C4C22×C22⋊D714yes—
812C2×C4C22×C22⋊D714yes—
813C7C2×#247111yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—144no—
823C22—144no—
824C22—144no—
825C22—282no—
826C22—2816no—
827C22—282no—
828C22—282no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—568no—
838C22#9021814yes—
839C22#9021814yes—
840C22#9021914yes—
841C22#9022614yes—
842C22#9048214yes—
843C22#9052014yes—
844C22#9052514yes—
845C22C22×#115711yescharacteristic
846C22C22×#115711yescharacteristic
847C22C2×D7×#4111yescharacteristic
848C22C2×D7×#4111yescharacteristic
849C22C2×#655311yescharacteristic
850C22C2×#655311yescharacteristic
851C22C23×C22⋊D711yescharacteristic
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#1173972418yesdirect product factor
868C2C2×#9021911yescharacteristic
869C2C2×#9022611yescharacteristic
870C2C2×#9021811yescharacteristic
871C2C2×#9021811yescharacteristic
872C2C2×#9048211yescharacteristic
873C2C2×#9052011yescharacteristic
874C2C2×#9052511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#117C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC22×#117D7
hypocenterC7C2×#2471
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×C7×#117C2semidirect
2. C22×#6457C2semidirect
3. C2×#89985C2semidirect
4. C2×#89985C2semidirect
5. #11739724C2direct (N × H)
6. C2×#89764C2semidirect
7. C2×#89765C2semidirect
8. C2×#89753C2semidirect
10. C2×#89728C2semidirect
11. C2×#89720C2semidirect
12. C2×#89729C2semidirect
13. C2×#89711C2semidirect
14. C2×#89712C2semidirect
15. C2×#89705C2semidirect
16. C2×C4×(C2×D7)⋊C4C2semidirect
23. C2×C7×#117C22semidirect
47. C2×#6457C22semidirect
48. #89985C22semidirect
49. #89985C22semidirect
58. #89765C22semidirect
59. #89764C22semidirect
60. #89753C22semidirect
62. #89729C22semidirect
63. #89728C22semidirect
64. #89720C22semidirect
65. #89712C22semidirect
66. #89711C22semidirect
67. C4×(C2×D7)⋊C4C22semidirect
68. #89705C22semidirect
107. C2×C7×C4⋊C4D4semidirect
160. C22×#117D7semidirect
269. C7×C4⋊C4C2×D4semidirect
298. C2×#117C2×D7semidirect
491. C2×C4⋊C4C22⋊D7semidirect
682. C4⋊C4C2×C22⋊D7semidirect
700. C2×C7#2471semidirect
813. C7C2×#2471semidirect
867. C2#11739724direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1172
C22×#64572
C2×#899852
#117397242
C2×#897642
C2×#897652
C2×#897532
C2×#897322
C2×#897282
C2×#897202
C2×#897292
C2×#897112
C2×#897122
C2×#897052
C2×C4×(C2×D7)⋊C42
C2×#24717