Finite Group Databasebeta

← C2×#11731351 #13521480

Subgroups — C2×#11731351 #13521480

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×C4×C22⋊D7C211yesmaximal, characteristic, complemented
2C22×#6461C211yesmaximal, characteristic, complemented
3C2×C7×#380C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5C2×#89764C211yesmaximal, characteristic, complemented
6C2×#89763C211yesmaximal, characteristic, complemented
7C2×#89750C211yesmaximal, characteristic, complemented
8C2×#89732C211yesmaximal, characteristic
9C2×#89733C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89717C211yesmaximal, characteristic, complemented
12#11731351C2116yesmaximal, direct product factor
13C2×#89437C211yesmaximal, characteristic, complemented
14C2×#89441C211yesmaximal, characteristic, complemented
15C2×#89427C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×D28C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C2×C4×C22⋊D7—28no—
29C2×C4×C22⋊D7C2218yescomplemented
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×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6461—28no—
47C2×#6461C2218yescomplemented
48C7×#380C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51#89985C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89764C2218yescomplemented
59#89763C2218yescomplemented
60#89750C2218yescomplemented
61#89733C2218yescomplemented
62#89732C2218yes—
63#89729C2218yescomplemented
64#89717C2218yescomplemented
65#89441C2218yescomplemented
66#89438C2218yescomplemented
67#89437C2218yescomplemented
68#89427C2218yescomplemented
69C2×#2467—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7—42no—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2314yes—
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—24no—
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—42no—
99C22×D28—42no—
100C22×D28C2314yes—
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—42no—
104C22×C4×D7C2314yes—
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4—42no—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C22⋊C4—42no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C4×C22⋊D7—232no—
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—24no—
124C2×(C2×D7)⋊C4—24no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4—42no—
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×(C2×D7)⋊C4C2314yes—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7C2314yes—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—42no—
140C2×Dic7⋊C4D418yescomplemented
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—24no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150#6461—232no—
151C7×#95C2314yes—
152C7×#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×C4×D4—71no—
161#2467—716no—
162C2×#399—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#392—71no—
166C2×#390—71no—
167C2×#388—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#387—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×#380D711yescharacteristic, complemented
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×C7—28no—
217C22×C4×C7—28no—
218C22×C4×C7—44no—
219C22×C4×C7—416no—
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—232no—
229C2×C22⋊D7—28no—
230C2×C22⋊D7—28no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—44no—
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×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—44no—
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⋊C4—44no—
270C7×C22⋊C4—44no—
271C7×C22⋊C4—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—28no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4—44no—
283C4⋊Dic7—28no—
284Dic7⋊C4—28no—
285Dic7⋊C4—44no—
286Dic7⋊C4C2×D4116yescomplemented
287C4×Dic7—28no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4—71no—
293C24×C4—71no—
294C24×C4C2×D711yescharacteristic
295C2×#126—78no—
296C2×#126—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⋊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×C42—71no—
320C22×C42—71no—
321#399—78no—
322#394—78no—
323#394—78no—
324#392—78no—
325#390—78no—
326#388—78no—
327#388—78no—
328#387—78no—
329#387—78no—
330#386—78no—
331#386—78no—
332#380C2×D718yescomplemented
333C4×C22⋊C4—78no—
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×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—416no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7—44no—
414C2×C4×C7—44no—
415C2×C4×C7C22×D414yes—
416C2×C4×C7C2×#4114yes—
417C22⋊D7—232no—
418C22⋊D7—416no—
419C2×Dic7—28no—
420C2×Dic7—28no—
421C2×Dic7—28no—
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×Dic7C22×D414yes—
441C2×Dic7C22×D414yes—
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—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×D714yes—
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#126—1432no—
481C4×D4—1432no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—78no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4—282no—
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
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—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
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#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#52514yes—
543C22×C7#52914yes—
544C22×C7#53814yes—
545C22×C7#54614yes—
546C22×C7#55014yes—
547C22×C7#55114yes—
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—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—1432no—
614C2×D4—148no—
615C2×D4—148no—
616C2×D4—284no—
617C2×D4—284no—
618C2×D4—2816no—
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—22no—
636C22×C4—22no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—44no—
640C22×C4—416no—
641C22×C4—74no—
642C22×C4—74no—
643C22×C4—74no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—148no—
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—142no—
666C22×C4—148no—
667C22×C4—284no—
668C22×C4—2816no—
669C22×C4#115714yes—
670C22×C4D4×D714yes—
671C22×C4C23×D712yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—28no—
678C4⋊C4—44no—
679C4⋊C4—716no—
680C4⋊C4—148no—
681C4⋊C4—148no—
682C4⋊C4—284no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—284no—
695C22⋊C4—284no—
696C42—148no—
697C42—148no—
698C42—284no—
699C2×C7—44no—
700C2×C7#246718yescomplemented
701C2×C7C2×#52511yescharacteristic
702C2×C7C2×#52911yescharacteristic
703C2×C7C2×#53811yescharacteristic
704C2×C7C2×#54611yescharacteristic
705C2×C7C2×#55011yescharacteristic
706C2×C7C2×#55111yescharacteristic
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—
751C23C2×#115712yes—
752C23C2×D4×D712yes—
753C23#654812yes—
754C23#654812yes—
755C23C2×#116114yes—
756C23C2×#116112yes—
757C23D7×#4112yes—
758C23D7×#4112yes—
759C23C24×D711yescharacteristic
760D4—1432no—
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—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—74no—
787C2×C4—74no—
788C2×C4—74no—
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×#115714yes—
812C2×C4C2×D4×D714yes—
813C7C2×#246711yescharacteristic, 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#9018114yes—
839C22#9020514yes—
840C22#9021914yes—
841C22#9029014yes—
842C22#9030414yes—
843C22#9031814yes—
844C22#9032814yes—
845C22C22×#115711yescharacteristic
846C22C22×D4×D711yescharacteristic
847C22C2×#654811yescharacteristic
848C22C2×#654811yescharacteristic
849C22C22×#116111yescharacteristic
850C22C2×D7×#4111yescharacteristic
851C22C2×D7×#4111yescharacteristic
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#1173135118yesdirect product factor
868C2C2×#9018111yescharacteristic
869C2C2×#9020511yescharacteristic
870C2C2×#9021911yescharacteristic
871C2C2×#9029011yescharacteristic
872C2C2×#9030411yescharacteristic
873C2C2×#9031811yescharacteristic
874C2C2×#9032811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#380C2
socleC24×C7C24
prime radicalC2×#89732C2
hypercenterC2×#380D7
hypocenterC7C2×#2467
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D7C2semidirect
2. C22×#6461C2semidirect
3. C2×C7×#380C2semidirect
4. C2×#89985C2semidirect
5. C2×#89764C2semidirect
6. C2×#89763C2semidirect
7. C2×#89750C2semidirect
9. C2×#89733C2semidirect
10. C2×#89729C2semidirect
11. C2×#89717C2semidirect
12. #11731351C2direct (N × H)
13. C2×#89437C2semidirect
14. C2×#89441C2semidirect
15. C2×#89427C2semidirect
16. C2×#89438C2semidirect
29. C2×C4×C22⋊D7C22semidirect
47. C2×#6461C22semidirect
48. C7×#380C22semidirect
51. #89985C22semidirect
58. #89764C22semidirect
59. #89763C22semidirect
60. #89750C22semidirect
61. #89733C22semidirect
63. #89729C22semidirect
64. #89717C22semidirect
65. #89441C22semidirect
66. #89438C22semidirect
67. #89437C22semidirect
68. #89427C22semidirect
140. C2×Dic7⋊C4D4semidirect
173. C2×#380D7semidirect
286. Dic7⋊C4C2×D4semidirect
332. #380C2×D7semidirect
700. C2×C7#2467semidirect
813. C7C2×#2467semidirect
867. C2#11731351direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C22×#64612
C2×C7×#3802
C2×#899852
C2×#897642
C2×#897632
C2×#897502
C2×#897322
C2×#897332
C2×#897292
C2×#897172
#117313512
C2×#894372
C2×#894412
C2×#894272
C2×#894382
C2×#24677