Finite Group Databasebeta

← C2×#11735001 #13520426

Subgroups — C2×#11735001 #13520426

Order 1792.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#397C211yesmaximal, characteristic, complemented
2C2×#89764C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
4C2×#89720C211yesmaximal, characteristic, complemented
5C2×#89733C211yesmaximal, characteristic
6C2×#89733C211yesmaximal, characteristic
7C2×#89729C211yesmaximal, characteristic
8C2×#89717C211yesmaximal, characteristic, complemented
9C2×#89723C211yesmaximal, characteristic, complemented
10#11735001C2116yesmaximal, direct product factor
11C2×#89433C211yesmaximal, characteristic, complemented
12C2×#89429C211yesmaximal, characteristic, complemented
13C2×#89446C211yesmaximal, characteristic, complemented
14C2×#89442C211yesmaximal, characteristic, complemented
15C2×#89441C211yesmaximal, characteristic, complemented
16C2×#89425C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C7×#397C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89764C2218yescomplemented
54C4⋊C4×Dic7C2218yescomplemented
55#89733C2218yes—
56#89733C2218yes—
57#89729C2218yes—
58#89723C2218yescomplemented
59#89720C2218yescomplemented
60#89717C2218yescomplemented
61#89446C2218yescomplemented
62#89442C2218yescomplemented
63#89441C2218yescomplemented
64#89433C2218yescomplemented
65#89429C2218yescomplemented
66#89425C2218yescomplemented
67C2×#2651—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C24×D7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C22×C22⋊D7—24no—
77C22×C22⋊D7—42no—
78C22×C22⋊D7—42no—
79C22×C22⋊D7C2314yes—
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C2×C7×C4⋊C4—24no—
88C2×C7×C4⋊C4C2314yes—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—42no—
91C2×C7×C22⋊C4—42no—
92C2×C7×C22⋊C4C2314yes—
93C2×C7×C22⋊C4C2314yes—
94C2×C7×C22⋊C4C2314yes—
95C2×C22⋊Dic7—24no—
96C2×C22⋊Dic7—42no—
97C2×C22⋊Dic7—42no—
98C2×C22⋊Dic7C2314yes—
99C2×C22⋊Dic7C2314yes—
100C2×C22⋊Dic7C2314yes—
101C2×(C2×D7)⋊C4—24no—
102C2×(C2×D7)⋊C4—24no—
103C2×(C2×D7)⋊C4—42no—
104C2×(C2×D7)⋊C4—42no—
105C2×(C2×D7)⋊C4—42no—
106C2×(C2×D7)⋊C4—42no—
107C2×(C2×D7)⋊C4C2314yes—
108C2×(C2×D7)⋊C4C2314yes—
109C2×(C2×D7)⋊C4C2314yes—
110C2×(C2×D7)⋊C4C2314yes—
111C2×(C2×D7)⋊C4C2314yes—
112C2×(C2×D7)⋊C4C2314yes—
113C2×C4⋊Dic7—24no—
114C2×C4⋊Dic7—24no—
115C2×C4⋊Dic7—42no—
116C2×C4⋊Dic7—42no—
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×C4⋊Dic7C2314yes—
120C2×C4⋊Dic7C2314yes—
121C2×Dic7⋊C4—42no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4—42no—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×C4×Dic7—24no—
130C2×C4×Dic7—42no—
131C2×C4×Dic7—42no—
132C2×C4×Dic7C2314yes—
133C2×C4×Dic7C2314yes—
134C2×C4×Dic7C2314yes—
135C7×#95C2314yes—
136C7×#95C2314yes—
137C7×#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145#2651—716no—
146C2×#399—71no—
147C2×#398—71no—
148C2×#398—71no—
149C2×#397—71no—
150C2×#397D711yescharacteristic, complemented
151C2×#396—71no—
152C2×#394—71no—
153C2×#394—71no—
154C2×#390—71no—
155C2×#388—71no—
156C2×#388—71no—
157C2×#388—71no—
158C2×#388—71no—
159C2×#387—71no—
160C2×C4×C4⋊C4—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7C2412yes—
169C24×C7C2411yescharacteristic
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7—22no—
175C23×D7—22no—
176C23×D7—22no—
177C23×D7C2412yes—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7#4114yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C2×C22⋊D7—28no—
203C2×C22⋊D7—44no—
204C2×C22⋊D7—44no—
205C2×C22⋊D7—416no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7#4114yes—
226C22×Dic7#4114yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C7×C4⋊C4—28no—
235C7×C22⋊C4—28no—
236C7×C22⋊C4—44no—
237C7×C22⋊C4—44no—
238C22⋊Dic7—28no—
239C22⋊Dic7—44no—
240C22⋊Dic7—44no—
241(C2×D7)⋊C4—28no—
242(C2×D7)⋊C4—28no—
243(C2×D7)⋊C4—44no—
244(C2×D7)⋊C4—44no—
245(C2×D7)⋊C4—44no—
246(C2×D7)⋊C4—44no—
247C4⋊Dic7—28no—
248C4⋊Dic7—28no—
249C4⋊Dic7—44no—
250C4⋊Dic7—44no—
251Dic7⋊C4—44no—
252Dic7⋊C4—44no—
253Dic7⋊C4—44no—
254Dic7⋊C4—44no—
255C4×Dic7—28no—
256C4×Dic7—44no—
257C4×Dic7—44no—
258C23×D4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊C4C2×D711yescharacteristic
268C22×C22⋊C4—71no—
269C22×C22⋊C4—71no—
270C22×C22⋊C4—71no—
271C22×C22⋊C4—71no—
272C22×C22⋊C4—71no—
273C22×C22⋊C4—71no—
274C22×C22⋊C4—71no—
275C22×C22⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C22⋊C4C2×D711yescharacteristic
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C22⋊C4C2×D711yescharacteristic
280C22×C42—71no—
281C22×C42—71no—
282C22×C42—71no—
283#399—78no—
284#398—78no—
285#398—78no—
286#397—78no—
287#397C2×D718yescomplemented
288#396—78no—
289#394—78no—
290#394—78no—
291#390—78no—
292#388—78no—
293#388—78no—
294#388—78no—
295#388—78no—
296#387—78no—
297C4×C4⋊C4—78no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95C2×D711yescharacteristic
306C2×#95C2×D711yescharacteristic
307C2×#95C2×D711yescharacteristic
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—44no—
316C23×C7—44no—
317C23×C7—44no—
318C23×C7—44no—
319C23×C7—44no—
320C23×C7—44no—
321C23×C7—44no—
322C23×C7C2×#4112yes—
323C23×C7C2×#4112yes—
324C23×C7C2×#4112yes—
325C23×C7H(5,𝔽2)12yes—
326C23×C7H(5,𝔽2)12yes—
327C23×C7H(5,𝔽2)12yes—
328C23×C72−1+412yes—
329C23×C7C2511yescharacteristic
330C22×D7—22no—
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—44no—
338C22×D7—44no—
339C22×D7—44no—
340C22×D7—44no—
341C22×D7—44no—
342C22×D7—44no—
343C22×D7—44no—
344C2×C4×C7—28no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—44no—
363C2×C4×C7—44no—
364C2×C4×C7—44no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×C4×C7C2×#4114yes—
368C22⋊D7—416no—
369C2×Dic7—28no—
370C2×Dic7—28no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—44no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7C2×#4114yes—
396C2×Dic7C2×#4114yes—
397C25—71no—
398C25C22×D711yescharacteristic
399C22×D4—74no—
400C22×D4—144no—
401C22×D4—282no—
402C22×D4—282no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413C23×C4C22×D711yescharacteristic
414C23×C4C22×D711yescharacteristic
415C23×C4C22×D711yescharacteristic
416C2×C4⋊C4—24no—
417C2×C4⋊C4—74no—
418C2×C4⋊C4—74no—
419C2×C4⋊C4—74no—
420C2×C4⋊C4—74no—
421C2×C4⋊C4—74no—
422C2×C4⋊C4—74no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—144no—
426C2×C4⋊C4—144no—
427C2×C4⋊C4—282no—
428C2×C4⋊C4—282no—
429C2×C4⋊C4—282no—
430C2×C4⋊C4—282no—
431C2×C4⋊C4—282no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22×D714yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—74no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—74no—
441C2×C22⋊C4—74no—
442C2×C22⋊C4—74no—
443C2×C22⋊C4—74no—
444C2×C22⋊C4—74no—
445C2×C22⋊C4—74no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—282no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4—282no—
452C2×C22⋊C4—282no—
453C2×C22⋊C4—282no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4C22×D714yes—
456C2×C22⋊C4C22×D714yes—
457C2×C22⋊C4C22×D714yes—
458C2×C42—74no—
459C2×C42—74no—
460C2×C42—74no—
461C2×C42—144no—
462C2×C42—282no—
463C2×C42—282no—
464#95—74no—
465#95—74no—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
470#95—74no—
471#95C22×D714yes—
472#95C22×D714yes—
473#95C22×D714yes—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—88no—
482C22×C7#52914yes—
483C22×C7#53814yes—
484C22×C7#53914yes—
485C22×C7#54014yes—
486C22×C7#54014yes—
487C22×C7#54214yes—
488C22×C7#54214yes—
489C22×C7C22×#4111yescharacteristic
490C22×C7C22×#4111yescharacteristic
491C22×C7C22×#4111yescharacteristic
492C22×C7C2×H(5,𝔽2)11yescharacteristic
493C22×C7C2×H(5,𝔽2)11yescharacteristic
494C22×C7C2×H(5,𝔽2)11yescharacteristic
495C22×C7C2×2−1+411yescharacteristic
496C2×D7—42no—
497C2×D7—42no—
498C2×D7—42no—
499C2×D7—42no—
500C2×D7—42no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—88no—
504C4×C7—24no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—42no—
510Dic7—24no—
511Dic7—24no—
512Dic7—42no—
513Dic7—42no—
514Dic7—42no—
515Dic7—42no—
516Dic7—42no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—72no—
525C24—142no—
526C24—142no—
527C24—142no—
528C24—142no—
529C24—142no—
530C24—142no—
531C24—142no—
532C24C23×D712yes—
533C24C23×D711yescharacteristic
534C2×D4—148no—
535C2×D4—284no—
536C2×D4—284no—
537C2×D4—2816no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—74no—
556C22×C4—74no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4#115914yes—
584C22×C4C23×D712yes—
585C22×C4C23×D712yes—
586C22×C4C23×D712yes—
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D712yes—
590C4⋊C4—28no—
591C4⋊C4—148no—
592C4⋊C4—148no—
593C4⋊C4—284no—
594C4⋊C4—284no—
595C4⋊C4—284no—
596C4⋊C4—284no—
597C4⋊C4—284no—
598C4⋊C4—284no—
599C22⋊C4—28no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—148no—
603C22⋊C4—148no—
604C22⋊C4—148no—
605C22⋊C4—284no—
606C22⋊C4—284no—
607C22⋊C4—284no—
608C22⋊C4—284no—
609C22⋊C4—284no—
610C22⋊C4—284no—
611C42—148no—
612C42—284no—
613C42—284no—
614C2×C7—82no—
615C2×C7#265118yescomplemented
616C2×C7C2×#52911yescharacteristic
617C2×C7C2×#53811yescharacteristic
618C2×C7C2×#53911yescharacteristic
619C2×C7C2×#54011yescharacteristic
620C2×C7C2×#54011yescharacteristic
621C2×C7C2×#54211yescharacteristic
622C2×C7C2×#54211yescharacteristic
623D7—82no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—142no—
639C23—142no—
640C23—142no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—284no—
646C23—284no—
647C23—284no—
648C23—284no—
649C23—284no—
650C23—284no—
651C23—284no—
652C23C2×#115912yes—
653C23#654812yes—
654C23D7×#4112yes—
655C23D7×#4112yes—
656C23#655312yes—
657C23#655312yes—
658C23#655412yes—
659C23C24×D711yescharacteristic
660D4—2816no—
661C2×C4—28no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—74no—
685C2×C4—74no—
686C2×C4—148no—
687C2×C4—148no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—284no—
708C2×C4—284no—
709C2×C4—284no—
710C2×C4—284no—
711C2×C4—284no—
712C2×C4C2×#115914yes—
713C7C2×#265111yescharacteristic, complemented, Sylow
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—88no—
722C22—282no—
723C22—282no—
724C22—282no—
725C22—282no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—568no—
730C22#9031014yes—
731C22#9034014yes—
732C22#9035314yes—
733C22#9035414yes—
734C22#9037314yes—
735C22#9039514yes—
736C22#9039814yes—
737C22C22×#115911yescharacteristic
738C22C2×#654811yescharacteristic
739C22C2×D7×#4111yescharacteristic
740C22C2×D7×#4111yescharacteristic
741C22C2×#655311yescharacteristic
742C22C2×#655311yescharacteristic
743C22C2×#655411yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—144no—
751C4—144no—
752C4—282no—
753C4—282no—
754C4—282no—
755C4—282no—
756C4—282no—
757C2—82no—
758C2—562no—
759C2#1173500118yesdirect product factor
760C2C2×#9031011yescharacteristic
761C2C2×#9034011yescharacteristic
762C2C2×#9035411yescharacteristic
763C2C2×#9035311yescharacteristic
764C2C2×#9037311yescharacteristic
765C2C2×#9039511yescharacteristic
766C2C2×#9039811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#397C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#397D7
hypocenterC7C2×#2651
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C7×#397C2semidirect
2. C2×#89764C2semidirect
3. C2×C4⋊C4×Dic7C2semidirect
4. C2×#89720C2semidirect
8. C2×#89717C2semidirect
9. C2×#89723C2semidirect
10. #11735001C2direct (N × H)
11. C2×#89433C2semidirect
12. C2×#89429C2semidirect
13. C2×#89446C2semidirect
14. C2×#89442C2semidirect
15. C2×#89441C2semidirect
16. C2×#89425C2semidirect
42. C7×#397C22semidirect
53. #89764C22semidirect
54. C4⋊C4×Dic7C22semidirect
58. #89723C22semidirect
59. #89720C22semidirect
60. #89717C22semidirect
61. #89446C22semidirect
62. #89442C22semidirect
63. #89441C22semidirect
64. #89433C22semidirect
65. #89429C22semidirect
66. #89425C22semidirect
150. C2×#397D7semidirect
287. #397C2×D7semidirect
615. C2×C7#2651semidirect
713. C7C2×#2651semidirect
759. C2#11735001direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3972
C2×#897642
C2×C4⋊C4×Dic72
C2×#897202
C2×#897332
C2×#897292
C2×#897172
C2×#897232
#117350012
C2×#894332
C2×#894292
C2×#894462
C2×#894422
C2×#894412
C2×#894252
C2×#26517