Finite Group Databasebeta

← C2×#11731846 #13516392

Subgroups — C2×#11731846 #13516392

Order 1792.

3302 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
2C2×C7×#385C211yesmaximal, characteristic, complemented
3C2×#89985C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5C2×#89759C211yesmaximal, characteristic, complemented
6C2×#89760C211yesmaximal, characteristic, complemented
7C2×#89762C211yesmaximal, characteristic, complemented
8C2×#89750C211yesmaximal, characteristic, complemented
9C2×#89728C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89723C211yesmaximal, characteristic, complemented
12#11731846C2116yesmaximal, direct product factor
13C2×#89437C211yesmaximal, characteristic, complemented
14C2×#89440C211yesmaximal, characteristic, complemented
15C2×#89436C211yesmaximal, characteristic, complemented
16C2×#89424C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6447C4116yescomplemented
43C2×#6447C2218yes—
44C7×#385C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47#89985C2218yescomplemented
48#89985C2218yescomplemented
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#89762C2218yescomplemented
58#89760C2218yescomplemented
59#89759C2218yescomplemented
60#89750C2218yescomplemented
61#89729C2218yescomplemented
62#89728C2218yescomplemented
63#89723C2218yescomplemented
64#89440C2218yescomplemented
65#89437C2218yescomplemented
66#89436C2218yescomplemented
67#89424C2218yescomplemented
68C2×#2377—71nomaximal, Sylow
69C25×C7C2311yescharacteristic
70C24×D7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7—42no—
73C23×C4×C7—42no—
74C23×C4×C7—42no—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2314yes—
82C22×C22⋊D7—42no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7C2×C418yes—
87C22×C22⋊D7C2×C418yescomplemented
88C22×C22⋊D7C2314yes—
89C22×C22⋊D7C2314yes—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C22×D28—42no—
97C22×D28—42no—
98C22×D28C2×C418yescomplemented
99C22×D28C2314yes—
100C22×C4×D7—42no—
101C22×C4×D7—42no—
102C22×C4×D7—42no—
103C22×C4×D7—42no—
104C22×C4×D7—42no—
105C22×C4×D7C2×C418yescomplemented
106C22×C4×D7C2314yes—
107C22×C4×D7C2314yes—
108C2×C7×C4⋊C4—42no—
109C2×C7×C4⋊C4—42no—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C22⋊C4—42no—
113C2×C7×C22⋊C4C2×C418yescomplemented
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C22⋊Dic7—42no—
117C2×C22⋊Dic7—42no—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×(C2×D7)⋊C4—42no—
121C2×(C2×D7)⋊C4—42no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4—42no—
127C2×(C2×D7)⋊C4C2×C418yescomplemented
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×C4⋊Dic7—42no—
137C2×C4⋊Dic7C2314yes—
138C2×Dic7⋊C4—42no—
139C2×Dic7⋊C4C2×C418yescomplemented
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×C4×Dic7—42no—
143C2×C4×Dic7—42no—
144C2×C4×Dic7C2314yes—
145C2×C4×Dic7C2314yes—
146#6447C2×C4164yescomplemented
147C7×#95C2314yes—
148C7×#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C22×#121—71no—
158#2377—716no—
159C2×#390—71no—
160C2×#390—71no—
161C2×#388—71no—
162C2×#388—71no—
163C2×#387—71no—
164C2×#387—71no—
165C2×#386—71no—
166C2×#386—71no—
167C2×#386—71no—
168C2×#386—71no—
169C2×#385—71no—
170C2×#385D711yescharacteristic, complemented
171C2×#381—71no—
172C2×#380—71no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7C22×C414yes—
180C24×C7C2412yes—
181C24×C7C2411yescharacteristic
182C23×D7—22no—
183C23×D7—22no—
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×D7C22×C414yes—
195C23×D7C22×C414yes—
196C23×D7C2412yes—
197C23×D7C2412yes—
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×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—44no—
215C22×C4×C7—44no—
216C22×C4×C7—44no—
217C22×C4×C7—416no—
218C22×C4×C7C22×C414yes—
219C22×C4×C7C22×C414yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C2×C22⋊D7—416no—
227C2×C22⋊D7—416no—
228C2×C22⋊D7—44no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—44no—
231C2×C22⋊D7—44no—
232C2×C22⋊D7C22×C4116yes—
233C2×C22⋊D7C22×C4116yescomplemented
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×Dic7C22×C414yes—
251C22×Dic7C22×C414yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C2×D28—416no—
259C2×D28—44no—
260C2×D28—44no—
261C2×D28C22×C4116yescomplemented
262C2×C4×D7—416no—
263C2×C4×D7—44no—
264C2×C4×D7—44no—
265C2×C4×D7—44no—
266C2×C4×D7—44no—
267C2×C4×D7—44no—
268C2×C4×D7—416no—
269C2×C4×D7C22×C4116yescomplemented
270C7×C4⋊C4—44no—
271C7×C4⋊C4—44no—
272C7×C22⋊C4—44no—
273C7×C22⋊C4C22×C4116yescomplemented
274C22⋊Dic7—44no—
275C22⋊Dic7—44no—
276(C2×D7)⋊C4—44no—
277(C2×D7)⋊C4—44no—
278(C2×D7)⋊C4—44no—
279(C2×D7)⋊C4—44no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4—44no—
283(C2×D7)⋊C4C22×C4116yescomplemented
284C4⋊Dic7—44no—
285Dic7⋊C4—44no—
286Dic7⋊C4C22×C4116yescomplemented
287C4×Dic7—44no—
288C4×Dic7—44no—
289C23×D4—71no—
290C23×D4—71no—
291C23×D4—71no—
292C24×C4—71no—
293C24×C4—71no—
294C24×C4C2×D711yescharacteristic
295C2×#121—716no—
296C2×#121—78no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4C2×D711yescharacteristic
301C22×C4⋊C4C2×D711yescharacteristic
302C22×C22⋊C4—71no—
303C22×C22⋊C4—71no—
304C22×C22⋊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⋊C4C2×D711yescharacteristic
313C22×C22⋊C4C2×D711yescharacteristic
314C22×C42—71no—
315C22×C42—71no—
316#390—78no—
317#390—78no—
318#388—78no—
319#388—78no—
320#387—78no—
321#387—78no—
322#386—78no—
323#386—78no—
324#386—78no—
325#386—78no—
326#385—78no—
327#385C2×D718yescomplemented
328#381—78no—
329#380—78no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C23×C7—28no—
341C23×C7—28no—
342C23×C7—28no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7C23×C414yes—
354C23×C7C23×C412yes—
355C23×C7H(5,𝔽2)12yes—
356C23×C7H(5,𝔽2)12yes—
357C23×C7H(5,𝔽2)12yes—
358C23×C7H(5,𝔽2)12yes—
359C23×C7H(5,𝔽2)12yes—
360C23×C72−1+412yes—
361C23×C7C2511yescharacteristic
362C22×D7—28no—
363C22×D7—28no—
364C22×D7—28no—
365C22×D7—28no—
366C22×D7—28no—
367C22×D7—28no—
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×D7C23×C414yes—
389C22×D7C23×C414yes—
390C2×C4×C7—28no—
391C2×C4×C7—28no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
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—416no—
409C2×C4×C7—44no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C23×C414yes—
414C2×C4×C7C23×C414yes—
415C22⋊D7—416no—
416C22⋊D7—416no—
417C2×Dic7—28no—
418C2×Dic7—28no—
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—44no—
436C2×Dic7—44no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7C23×C414yes—
440C2×Dic7C23×C414yes—
441D28—416no—
442C4×D7—416no—
443C4×D7—416no—
444C25—71no—
445C25—71no—
446C25C22×D711yescharacteristic
447C22×D4—78no—
448C22×D4—78no—
449C22×D4—74no—
450C22×D4—74no—
451C22×D4—78no—
452C22×D4—74no—
453C22×D4—282no—
454C22×D4—282no—
455C22×D4—282no—
456C22×D4—282no—
457C22×D4—282no—
458C22×D4—282no—
459C23×C4—42no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—78no—
465C23×C4—74no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—74no—
471C23×C4—282no—
472C23×C4—282no—
473C23×C4—282no—
474C23×C4—282no—
475C23×C4—282no—
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D714yes—
483#121—764no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—78no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—282no—
491C2×C4⋊C4—282no—
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—78no—
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—282no—
507C2×C22⋊C4—282no—
508C2×C22⋊C4—282no—
509C2×C22⋊C4—282no—
510C2×C22⋊C4—282no—
511C2×C22⋊C4—282no—
512C2×C22⋊C4—282no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4C4×D718yescomplemented
516C2×C22⋊C4C22×D714yes—
517C2×C22⋊C4C22×D714yes—
518C2×C42—74no—
519C2×C42—74no—
520C2×C42—282no—
521C2×C42—282no—
522#95—74no—
523#95—74no—
524#95—74no—
525#95—74no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95C22×D714yes—
531#95C22×D714yes—
532C22×C7—24no—
533C22×C7—24no—
534C22×C7—24no—
535C22×C7—416no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7#51814yes—
541C22×C7#51814yes—
542C22×C7#52014yes—
543C22×C7#56014yes—
544C22×C7#56014yes—
545C22×C7#56214yes—
546C22×C7#56214yes—
547C22×C7C24×C411yescharacteristic
548C22×C7C2×H(5,𝔽2)11yescharacteristic
549C22×C7C2×H(5,𝔽2)11yescharacteristic
550C22×C7C2×H(5,𝔽2)11yescharacteristic
551C22×C7C2×H(5,𝔽2)11yescharacteristic
552C22×C7C2×H(5,𝔽2)11yescharacteristic
553C22×C7C2×2−1+411yescharacteristic
554C2×D7—24no—
555C2×D7—24no—
556C2×D7—24no—
557C2×D7—24no—
558C2×D7—24no—
559C2×D7—24no—
560C2×D7—416no—
561C2×D7—416no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C4×C7—24no—
571C4×C7—24no—
572C4×C7—42no—
573C4×C7—42no—
574C4×C7—42no—
575C4×C7—42no—
576Dic7—24no—
577Dic7—24no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—74no—
589C24—74no—
590C24—72no—
591C24—72no—
592C24—142no—
593C24—142no—
594C24—142no—
595C24—142no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24C2×C4×D714yes—
605C24C23×D712yes—
606C24C23×D711yescharacteristic
607C2×D4—716no—
608C2×D4—716no—
609C2×D4—716no—
610C2×D4—2816no—
611C2×D4—284no—
612C2×D4—284no—
613C2×D4—2816no—
614C2×D4—2816no—
615C2×D4—284no—
616C2×D4—284no—
617C2×D4—284no—
618C2×D4—284no—
619C22×C4—22no—
620C22×C4—22no—
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—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—416no—
639C22×C4—74no—
640C22×C4—74no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—716no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
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—2816no—
665C22×C4—284no—
666C22×C4—284no—
667C22×C4—284no—
668C22×C4—284no—
669C22×C4—284no—
670C22×C4—2816no—
671C22×C4C2×C4×D714yes—
672C22×C4C2×C4×D714yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C22×C4C23×D712yes—
678C22×C4C23×D712yes—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—716no—
682C4⋊C4—284no—
683C4⋊C4—284no—
684C22⋊C4—44no—
685C22⋊C4—716no—
686C22⋊C4—284no—
687C22⋊C4—284no—
688C22⋊C4—284no—
689C22⋊C4—284no—
690C22⋊C4—284no—
691C22⋊C4—284no—
692C22⋊C4—284no—
693C22⋊C4—284no—
694C22⋊C4—284no—
695C22⋊C4C2×C4×D7116yescomplemented
696C42—284no—
697C42—284no—
698C2×C7—44no—
699C2×C7#237718yescomplemented
700C2×C7C2×#51811yescharacteristic
701C2×C7C2×#51811yescharacteristic
702C2×C7C2×#52011yescharacteristic
703C2×C7C2×#56011yescharacteristic
704C2×C7C2×#56011yescharacteristic
705C2×C7C2×#56211yescharacteristic
706C2×C7C2×#56211yescharacteristic
707D7—44no—
708D7—44no—
709C23—28no—
710C23—28no—
711C23—28no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—74no—
723C23—74no—
724C23—148no—
725C23—148no—
726C23—148no—
727C23—148no—
728C23—148no—
729C23—148no—
730C23—142no—
731C23—142no—
732C23—142no—
733C23—142no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—284no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23C22×C4×D714yes—
751C23C22×C4×D712yes—
752C23#654812yes—
753C23#654812yes—
754C23#654812yes—
755C23#655112yes—
756C23#655312yes—
757C23#655312yes—
758C23C24×D711yescharacteristic
759D4—2816no—
760D4—2816no—
761D4—2816no—
762C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—416no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—74no—
786C2×C4—74no—
787C2×C4—148no—
788C2×C4—148no—
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×C4C22×C4×D714yes—
812C2×C4C22×C4×D714yes—
813C7C2×#237711yescharacteristic, 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—144no—
826C22—144no—
827C22—144no—
828C22—282no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—2816no—
837C22—2816no—
838C22#9019514yes—
839C22#9023614yes—
840C22#9023614yes—
841C22#9028614yes—
842C22#9033814yes—
843C22#9033814yes—
844C22#9035714yes—
845C22C23×C4×D711yescharacteristic
846C22C2×#654811yescharacteristic
847C22C2×#654811yescharacteristic
848C22C2×#654811yescharacteristic
849C22C2×#655111yescharacteristic
850C22C2×#655311yescharacteristic
851C22C2×#655311yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—144no—
859C4—144no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—284no—
866C2—284no—
867C2#1173184618yesdirect product factor
868C2C2×#9019511yescharacteristic
869C2C2×#9023611yescharacteristic
870C2C2×#9023611yescharacteristic
871C2C2×#9028611yescharacteristic
872C2C2×#9033811yescharacteristic
873C2C2×#9033811yescharacteristic
874C2C2×#9035711yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC22×#6447C2
cosocleC23×C7C25
hypercenterC2×#385D7
hypocenterC7C2×#2377
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×C7×#385C2semidirect
3. C2×#89985C2semidirect
4. C2×#89985C2semidirect
5. C2×#89759C2semidirect
6. C2×#89760C2semidirect
7. C2×#89762C2semidirect
8. C2×#89750C2semidirect
9. C2×#89728C2semidirect
10. C2×#89729C2semidirect
11. C2×#89723C2semidirect
12. #11731846C2direct (N × H)
13. C2×#89437C2semidirect
14. C2×#89440C2semidirect
15. C2×#89436C2semidirect
16. C2×#89424C2semidirect
42. C2×#6447C4semidirect
44. C7×#385C22semidirect
47. #89985C22semidirect
48. #89985C22semidirect
57. #89762C22semidirect
58. #89760C22semidirect
59. #89759C22semidirect
60. #89750C22semidirect
61. #89729C22semidirect
62. #89728C22semidirect
63. #89723C22semidirect
64. #89440C22semidirect
65. #89437C22semidirect
66. #89436C22semidirect
67. #89424C22semidirect
87. C22×C22⋊D7C2×C4semidirect
98. C22×D28C2×C4semidirect
105. C22×C4×D7C2×C4semidirect
113. C2×C7×C22⋊C4C2×C4semidirect
127. C2×(C2×D7)⋊C4C2×C4semidirect
139. C2×Dic7⋊C4C2×C4semidirect
146. #6447C2×C4semidirect
170. C2×#385D7semidirect
233. C2×C22⋊D7C22×C4semidirect
261. C2×D28C22×C4semidirect
269. C2×C4×D7C22×C4semidirect
273. C7×C22⋊C4C22×C4semidirect
283. (C2×D7)⋊C4C22×C4semidirect
286. Dic7⋊C4C22×C4semidirect
327. #385C2×D7semidirect
515. C2×C22⋊C4C4×D7semidirect
695. C22⋊C4C2×C4×D7semidirect
699. C2×C7#2377semidirect
813. C7C2×#2377semidirect
867. C2#11731846direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64472
C2×C7×#3852
C2×#899852
C2×#897592
C2×#897602
C2×#897622
C2×#897502
C2×#897282
C2×#897292
C2×#897232
#117318462
C2×#894372
C2×#894402
C2×#894362
C2×#894242
C2×#23777