Finite Group Databasebeta

← C2×#11733466 #13522012

Subgroups — C2×#11733466 #13522012

Order 1792.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6461C211yesmaximal, characteristic
2C22×C4×Dic14C211yesmaximal, characteristic, complemented
3C2×C7×#389C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic
5C2×#89754C211yesmaximal, characteristic, complemented
6C2×#89762C211yesmaximal, characteristic
7C2×#89762C211yesmaximal, characteristic
8C2×#89750C211yesmaximal, characteristic, complemented
9C2×#89753C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
11C2×#89712C211yesmaximal, characteristic
12#11733466C2116yesmaximal, direct product factor
13C2×#89445C211yesmaximal, characteristic
14C2×#89428C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic
16C2×#89427C211yesmaximal, characteristic, complemented
17C23×Dic14C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6461—28no—
41C2×#6461C2218yes—
42C2×C4×Dic14—28no—
43C2×C4×Dic14C2218yescomplemented
44C7×#389C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
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#89766C2218yes—
58#89762C2218yes—
59#89762C2218yes—
60#89754C2218yescomplemented
61#89753C2218yescomplemented
62#89750C2218yescomplemented
63C4⋊C4×Dic7C2218yescomplemented
64#89712C2218yes—
65#89445C2218yes—
66#89442C2218yes—
67#89428C2218yescomplemented
68#89427C2218yescomplemented
69C2×#2469—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×Dic14—24no—
86C22×Dic14—24no—
87C22×Dic14—24no—
88C22×Dic14C2314yes—
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4—24no—
91C2×C7×C4⋊C4—24no—
92C2×C7×C4⋊C4—24no—
93C2×C7×C4⋊C4C2314yes—
94C2×C7×C4⋊C4C2314yes—
95C2×C7×C4⋊C4C2314yes—
96C2×C7×C4⋊C4C2314yes—
97C2×C42×C7—24no—
98C2×C42×C7C2314yes—
99C2×(C2×D7)⋊C4—24no—
100C2×(C2×D7)⋊C4—24no—
101C2×(C2×D7)⋊C4—24no—
102C2×(C2×D7)⋊C4—24no—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4C2314yes—
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—24no—
116C2×C4⋊Dic7C2314yes—
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4D418yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×C4×Dic7—24no—
126C2×C4×Dic7—24no—
127C2×C4×Dic7—24no—
128C2×C4×Dic7—24no—
129C2×C4×Dic7C2314yes—
130C2×C4×Dic7C2314yes—
131C2×C4×Dic7C2314yes—
132C2×C4×Dic7C2314yes—
133#6461—232no—
134C4×Dic14—232no—
135C7×#95C2314yes—
136C7×#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C22×#126—71no—
148C22×C4×Q8—71no—
149#2469—716no—
150C2×#400—71no—
151C2×#396—71no—
152C2×#395—71no—
153C2×#393—71no—
154C2×#389D711yescharacteristic, complemented
155C2×#388—71no—
156C2×#388—71no—
157C2×#388—71no—
158C2×#388—71no—
159C2×#387—71no—
160C2×#387—71no—
161C2×#387—71no—
162C2×C4×C4⋊C4—71no—
163C24×C7C2411yescharacteristic
164C23×D7—22no—
165C23×D7—22no—
166C23×D7—22no—
167C23×D7—22no—
168C23×D7—22no—
169C23×D7—22no—
170C23×D7—22no—
171C23×D7C2412yes—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
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×C7C2×D414yes—
190C22×C4×C7#4114yes—
191C22×C4×C7#4114yes—
192C22×C4×C7#4114yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
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×Dic7C2×D414yes—
219C22×Dic7C2×D414yes—
220C22×Dic7#4114yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C2×Dic14—232no—
229C2×Dic14—28no—
230C2×Dic14—28no—
231C2×Dic14—28no—
232C7×C4⋊C4—28no—
233C7×C4⋊C4—28no—
234C7×C4⋊C4—28no—
235C7×C4⋊C4—28no—
236C42×C7—28no—
237(C2×D7)⋊C4—28no—
238(C2×D7)⋊C4—28no—
239(C2×D7)⋊C4—28no—
240(C2×D7)⋊C4—28no—
241(C2×D7)⋊C4—28no—
242(C2×D7)⋊C4—28no—
243(C2×D7)⋊C4—28no—
244C4⋊Dic7—28no—
245C4⋊Dic7—28no—
246C4⋊Dic7—28no—
247Dic7⋊C4—28no—
248Dic7⋊C4—28no—
249Dic7⋊C4C2×D4116yes—
250C4×Dic7—28no—
251C4×Dic7—28no—
252C4×Dic7—28no—
253C4×Dic7—28no—
254C23×Q8—71no—
255C2×#126—78no—
256C2×#126—148no—
257C2×C4×Q8—78no—
258C2×C4×Q8—148no—
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⋊C4C2×D711yescharacteristic
266C22×C4⋊C4C2×D711yescharacteristic
267C22×C4⋊C4C2×D711yescharacteristic
268C22×C4⋊C4C2×D711yescharacteristic
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×C42—71no—
277C22×C42—71no—
278C22×C42—71no—
279C22×C42—71no—
280C22×C42C2×D711yescharacteristic
281#400—78no—
282#396—78no—
283#395—78no—
284#393—78no—
285#389C2×D718yescomplemented
286#388—78no—
287#388—78no—
288#388—78no—
289#388—78no—
290#387—78no—
291#387—78no—
292#387—78no—
293C4×C4⋊C4—78no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95C2×D711yescharacteristic
305C2×#95C2×D711yescharacteristic
306C23×C7C22×D412yes—
307C23×C7C2×#4112yes—
308C23×C7C2×#4112yes—
309C23×C7C2×#4112yes—
310C23×C7C2×#4112yes—
311C23×C72−1+412yes—
312C23×C72−1+412yes—
313C23×C7C2511yescharacteristic
314C22×D7—22no—
315C22×D7—22no—
316C22×D7—22no—
317C22×D7—22no—
318C22×D7—22no—
319C22×D7—22no—
320C22×D7—22no—
321C22×D7—44no—
322C22×D7—44no—
323C22×D7—44no—
324C22×D7—44no—
325C22×D7—44no—
326C22×D7—44no—
327C22×D7—44no—
328C2×C4×C7—28no—
329C2×C4×C7—28no—
330C2×C4×C7—28no—
331C2×C4×C7—28no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—44no—
350C2×C4×C7—44no—
351C2×C4×C7—44no—
352C2×C4×C7C22×D414yes—
353C2×C4×C7C2×#4114yes—
354C2×C4×C7C2×#4114yes—
355C2×C4×C7C2×#4114yes—
356C2×Dic7—28no—
357C2×Dic7—28no—
358C2×Dic7—28no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—44no—
378C2×Dic7—44no—
379C2×Dic7—44no—
380C2×Dic7—44no—
381C2×Dic7C22×D414yes—
382C2×Dic7C22×D414yes—
383C2×Dic7C2×#4114yes—
384Dic14—232no—
385C25—71no—
386C22×Q8—74no—
387C22×Q8—144no—
388C22×Q8—144no—
389C22×Q8—144no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4—71no—
395C23×C4—71no—
396C23×C4—71no—
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404#126—1432no—
405C4×Q8—1432no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—78no—
411C2×C4⋊C4—74no—
412C2×C4⋊C4—74no—
413C2×C4⋊C4—74no—
414C2×C4⋊C4—74no—
415C2×C4⋊C4—74no—
416C2×C4⋊C4—74no—
417C2×C4⋊C4—144no—
418C2×C4⋊C4—144no—
419C2×C4⋊C4—144no—
420C2×C4⋊C4—144no—
421C2×C4⋊C4—144no—
422C2×C4⋊C4C22×D714yes—
423C2×C4⋊C4C22×D714yes—
424C2×C4⋊C4C22×D714yes—
425C2×C4⋊C4C22×D714yes—
426C2×C22⋊C4—74no—
427C2×C22⋊C4—74no—
428C2×C22⋊C4—74no—
429C2×C22⋊C4—74no—
430C2×C22⋊C4—74no—
431C2×C22⋊C4—74no—
432C2×C22⋊C4—74no—
433C2×C22⋊C4—144no—
434C2×C22⋊C4—144no—
435C2×C22⋊C4—144no—
436C2×C22⋊C4—144no—
437C2×C22⋊C4—144no—
438C2×C22⋊C4—144no—
439C2×C22⋊C4—144no—
440C2×C42—24no—
441C2×C42—74no—
442C2×C42—74no—
443C2×C42—74no—
444C2×C42—74no—
445C2×C42—144no—
446C2×C42—144no—
447C2×C42—144no—
448C2×C42—144no—
449C2×C42C22×D714yes—
450#95—74no—
451#95—74no—
452#95—74no—
453#95—74no—
454#95—74no—
455#95—74no—
456#95—74no—
457#95—74no—
458#95—74no—
459#95—74no—
460#95C22×D714yes—
461#95C22×D714yes—
462C22×C7#52514yes—
463C22×C7#52914yes—
464C22×C7#54114yes—
465C22×C7#54714yes—
466C22×C7#54814yes—
467C22×C7#55614yes—
468C22×C7#55614yes—
469C22×C7C23×D411yescharacteristic
470C22×C7C22×#4111yescharacteristic
471C22×C7C22×#4111yescharacteristic
472C22×C7C22×#4111yescharacteristic
473C22×C7C22×#4111yescharacteristic
474C22×C7C2×2−1+411yescharacteristic
475C22×C7C2×2−1+411yescharacteristic
476C2×D7—42no—
477C2×D7—42no—
478C2×D7—42no—
479C2×D7—42no—
480C2×D7—42no—
481C2×D7—42no—
482C2×D7—42no—
483C2×D7—88no—
484C4×C7—24no—
485C4×C7—24no—
486C4×C7—24no—
487C4×C7—24no—
488C4×C7—42no—
489C4×C7—42no—
490C4×C7—42no—
491Dic7—24no—
492Dic7—24no—
493Dic7—24no—
494Dic7—42no—
495Dic7—42no—
496Dic7—42no—
497Dic7—42no—
498C24—72no—
499C24—142no—
500C24—142no—
501C24—142no—
502C24—142no—
503C24—142no—
504C24—142no—
505C24—142no—
506C24C23×D711yescharacteristic
507C2×Q8—148no—
508C2×Q8—148no—
509C2×Q8—1432no—
510C2×Q8—148no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—74no—
529C22×C4—74no—
530C22×C4—74no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—72no—
534C22×C4—72no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—142no—
539C22×C4—142no—
540C22×C4—142no—
541C22×C4—142no—
542C22×C4—142no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4#115714yes—
557C22×C4D4×D714yes—
558C22×C4#115914yes—
559C22×C4#116114yes—
560C22×C4C23×D712yes—
561C22×C4C23×D712yes—
562C22×C4C23×D712yes—
563C22×C4C23×D712yes—
564C22×C4C23×D712yes—
565C22×C4C23×D712yes—
566C22×C4C23×D712yes—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—716no—
572C4⋊C4—148no—
573C4⋊C4—148no—
574C4⋊C4—148no—
575C4⋊C4—148no—
576C4⋊C4—148no—
577C22⋊C4—148no—
578C22⋊C4—148no—
579C22⋊C4—148no—
580C22⋊C4—148no—
581C22⋊C4—148no—
582C22⋊C4—148no—
583C22⋊C4—148no—
584C42—28no—
585C42—148no—
586C42—148no—
587C42—148no—
588C42—148no—
589C2×C7#246918yescomplemented
590C2×C7C2×#52511yescharacteristic
591C2×C7C2×#52911yescharacteristic
592C2×C7C2×#54111yescharacteristic
593C2×C7C2×#54711yescharacteristic
594C2×C7C2×#54811yescharacteristic
595C2×C7C2×#55611yescharacteristic
596C2×C7C2×#55611yescharacteristic
597D7—82no—
598C23—142no—
599C23—142no—
600C23—142no—
601C23—142no—
602C23—142no—
603C23—142no—
604C23—142no—
605C23—284no—
606C23—284no—
607C23—284no—
608C23—284no—
609C23—284no—
610C23—284no—
611C23—284no—
612C23C2×#115712yes—
613C23C2×D4×D712yes—
614C23C2×#115912yes—
615C23C2×#116112yes—
616C23#655112yes—
617C23D7×#4112yes—
618C23#655412yes—
619C23C24×D711yescharacteristic
620Q8—1432no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—74no—
646C2×C4—74no—
647C2×C4—74no—
648C2×C4—148no—
649C2×C4—148no—
650C2×C4—148no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—142no—
654C2×C4—142no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—284no—
670C2×C4—284no—
671C2×C4—284no—
672C2×C4—284no—
673C2×C4C2×#115714yes—
674C2×C4C2×D4×D714yes—
675C2×C4C2×#115914yes—
676C2×C4C2×#116114yes—
677C7C2×#246911yescharacteristic, complemented, Sylow
678C22—282no—
679C22—282no—
680C22—282no—
681C22—282no—
682C22—282no—
683C22—282no—
684C22—282no—
685C22—568no—
686C22#9019814yes—
687C22#9022914yes—
688C22#9027514yes—
689C22#9028914yes—
690C22#9031814yes—
691C22#9038714yes—
692C22#9042314yes—
693C22C22×#115711yescharacteristic
694C22C22×D4×D711yescharacteristic
695C22C22×#115911yescharacteristic
696C22C22×#116111yescharacteristic
697C22C2×#655111yescharacteristic
698C22C2×D7×#4111yescharacteristic
699C22C2×#655411yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—144no—
708C4—144no—
709C4—144no—
710C4—282no—
711C4—282no—
712C4—282no—
713C4—282no—
714C2—562no—
715C2#1173346618yesdirect product factor
716C2C2×#9019811yescharacteristic
717C2C2×#9022911yescharacteristic
718C2C2×#9027511yescharacteristic
719C2C2×#9028911yescharacteristic
720C2C2×#9031811yescharacteristic
721C2C2×#9038711yescharacteristic
722C2C2×#9042311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#389C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#389D7
hypocenterC7C2×#2469
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic14C2semidirect
3. C2×C7×#389C2semidirect
5. C2×#89754C2semidirect
8. C2×#89750C2semidirect
9. C2×#89753C2semidirect
10. C2×C4⋊C4×Dic7C2semidirect
12. #11733466C2direct (N × H)
14. C2×#89428C2semidirect
16. C2×#89427C2semidirect
43. C2×C4×Dic14C22semidirect
44. C7×#389C22semidirect
60. #89754C22semidirect
61. #89753C22semidirect
62. #89750C22semidirect
63. C4⋊C4×Dic7C22semidirect
67. #89428C22semidirect
68. #89427C22semidirect
154. C2×#389D7semidirect
285. #389C2×D7semidirect
589. C2×C7#2469semidirect
677. C7C2×#2469semidirect
715. C2#11733466direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64612
C22×C4×Dic142
C2×C7×#3892
C2×#897662
C2×#897542
C2×#897622
C2×#897502
C2×#897532
C2×C4⋊C4×Dic72
C2×#897122
#117334662
C2×#894452
C2×#894282
C2×#894422
C2×#894272
C2×#24697