Finite Group Databasebeta

← C2×#11735465 #13521797

Subgroups — C2×#11735465 #13521797

Order 1792.

2790 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6450C211yesmaximal, characteristic, complemented
2C22×#6441C211yesmaximal, characteristic
3C2×C7×#399C211yesmaximal, characteristic
4C2×#89752C211yesmaximal, characteristic, complemented
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89744C211yesmaximal, characteristic, complemented
7C2×#89753C211yesmaximal, characteristic, complemented
8C2×#89748C211yesmaximal, characteristic, complemented
9C2×#89721C211yesmaximal, characteristic
10C2×#89717C211yesmaximal, characteristic
11C2×#89716C211yesmaximal, characteristic
12C2×#89714C211yesmaximal, characteristic
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic
14#11735465C2116yesmaximal, direct product factor
15C2×#89418C211yesmaximal, characteristic, complemented
16C2×#89425C211yesmaximal, characteristic, complemented
17C24×Dic7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6450—28no—
43C2×#6450C2218yescomplemented
44C2×#6441—28no—
45C2×#6441C2218yes—
46C7×#399C2218yes—
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#89756C2218yescomplemented
58#89753C2218yescomplemented
59#89752C2218yescomplemented
60#89748C2218yescomplemented
61#89744C2218yescomplemented
62#89721C2218yes—
63#89717C2218yes—
64#89716C2218yes—
65#89714C2218yes—
66C22⋊C4×Dic7C2218yes—
67#89425C2218yescomplemented
68#89418C2218yescomplemented
69C2×#2423—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×Dic7—24no—
78C23×Dic7—24no—
79C23×Dic7—24no—
80C23×Dic7C2314yes—
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C22×Dic14—24no—
90C22×Dic14—24no—
91C22×Dic14D418yes—
92C22×Dic14C2314yes—
93C2×C7×C4⋊C4—24no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—42no—
96C2×C7×C4⋊C4C2314yes—
97C2×C7×C4⋊C4C2314yes—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C22⋊Dic7—24no—
106C2×C22⋊Dic7—42no—
107C2×C22⋊Dic7Q818yescomplemented
108C2×C22⋊Dic7C2314yes—
109C2×C22⋊Dic7C2314yes—
110C2×C22⋊Dic7C2314yes—
111C2×C4⋊Dic7—24no—
112C2×C4⋊Dic7—24no—
113C2×C4⋊Dic7C2314yes—
114C2×C4⋊Dic7C2314yes—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—42no—
121C2×Dic7⋊C4—42no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×C4×Dic7—24no—
132C2×C4×Dic7—24no—
133C2×C4×Dic7—24no—
134C2×C4×Dic7—24no—
135C2×C4×Dic7C2314yes—
136C2×C4×Dic7C2314yes—
137C2×C4×Dic7C2314yes—
138C2×C4×Dic7C2314yes—
139#6450—232no—
140#6441—232no—
141C7×#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C22×C22⋊Q8—71no—
152C22×C4×Q8—71no—
153#2423—716no—
154C2×#399—71no—
155C2×#399D711yescharacteristic
156C2×#398—71no—
157C2×#398—71no—
158C2×#391—71no—
159C2×#389—71no—
160C2×#388—71no—
161C2×#388—71no—
162C2×#387—71no—
163C2×#387—71no—
164C2×#384—71no—
165C2×#380—71no—
166C2×C4×C22⋊C4—71no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7C2×Q814yes—
174C24×C7C2412yes—
175C24×C7C2411yescharacteristic
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×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7C2×D414yes—
193C22×C4×C7#4114yes—
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×Dic7—28no—
219C22×Dic7—28no—
220C22×Dic7—28no—
221C22×Dic7—416no—
222C22×Dic7C2×D414yes—
223C22×Dic7C2×D414yes—
224C22×Dic7C2×Q814yes—
225C22×Dic7C2×Q814yes—
226C22×Dic7#4114yes—
227C22×Dic7#4114yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C2×Dic14—232no—
237C2×Dic14—28no—
238C2×Dic14—28no—
239C2×Dic14C2×D4116yes—
240C7×C4⋊C4—28no—
241C7×C4⋊C4—28no—
242C7×C4⋊C4—44no—
243C7×C22⋊C4—28no—
244C7×C22⋊C4—28no—
245C7×C22⋊C4—44no—
246C22⋊Dic7—28no—
247C22⋊Dic7—44no—
248C22⋊Dic7C2×Q8116yescomplemented
249C4⋊Dic7—28no—
250C4⋊Dic7—28no—
251Dic7⋊C4—28no—
252Dic7⋊C4—28no—
253Dic7⋊C4—28no—
254Dic7⋊C4—28no—
255Dic7⋊C4—28no—
256Dic7⋊C4—44no—
257Dic7⋊C4—44no—
258Dic7⋊C4—44no—
259C4×Dic7—28no—
260C4×Dic7—28no—
261C4×Dic7—28no—
262C4×Dic7—28no—
263C23×Q8—71no—
264C24×C4—71no—
265C2×C22⋊Q8—78no—
266C2×C22⋊Q8—148no—
267C2×C4×Q8—78no—
268C2×C4×Q8—148no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4—71no—
273C22×C4⋊C4—71no—
274C22×C4⋊C4—71no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4C2×D711yescharacteristic
280C22×C4⋊C4C2×D711yescharacteristic
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C22⋊C4—71no—
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4C2×D711yescharacteristic
286C22×C22⋊C4C2×D711yescharacteristic
287C22×C22⋊C4C2×D711yescharacteristic
288C22×C42—71no—
289C22×C42—71no—
290C22×C42—71no—
291C22×C42—71no—
292#399—78no—
293#399C2×D718yes—
294#398—78no—
295#398—78no—
296#391—78no—
297#389—78no—
298#388—78no—
299#388—78no—
300#387—78no—
301#387—78no—
302#384—78no—
303#380—78no—
304C4×C22⋊C4—78no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95C2×D711yescharacteristic
315C23×C7—28no—
316C23×C7—28no—
317C23×C7—28no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—44no—
325C23×C7—44no—
326C23×C7—44no—
327C23×C7—44no—
328C23×C7C22×D412yes—
329C23×C7C22×Q814yes—
330C23×C7C22×Q812yes—
331C23×C7C2×#4112yes—
332C23×C7C2×#4112yes—
333C23×C7C2×#4112yes—
334C23×C7H(5,𝔽2)12yes—
335C23×C72−1+412yes—
336C23×C7C2511yescharacteristic
337C2×C4×C7—28no—
338C2×C4×C7—28no—
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—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—44no—
356C2×C4×C7—44no—
357C2×C4×C7—44no—
358C2×C4×C7—44no—
359C2×C4×C7C22×D414yes—
360C2×C4×C7C2×#4114yes—
361C2×Dic7—28no—
362C2×Dic7—28no—
363C2×Dic7—28no—
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—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—44no—
383C2×Dic7—44no—
384C2×Dic7—44no—
385C2×Dic7—44no—
386C2×Dic7—416no—
387C2×Dic7#123116yes—
388C2×Dic7C22×D414yes—
389C2×Dic7C22×D414yes—
390C2×Dic7C22×Q814yes—
391C2×Dic7C22×Q814yes—
392C2×Dic7C2×#4114yes—
393C2×Dic7C2×#4114yes—
394Dic14—232no—
395C25C22×D711yescharacteristic
396C22×Q8—78no—
397C22×Q8—74no—
398C22×Q8—144no—
399C22×Q8—144no—
400C23×C4—71no—
401C23×C4—71no—
402C23×C4—71no—
403C23×C4—71no—
404C23×C4—74no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—144no—
410C23×C4—144no—
411C23×C4—144no—
412C23×C4C22×D711yescharacteristic
413C23×C4C22×D711yescharacteristic
414C23×C4C22×D711yescharacteristic
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D711yescharacteristic
417C23×C4C22×D711yescharacteristic
418C22⋊Q8—1432no—
419C4×Q8—1432no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—74no—
426C2×C4⋊C4—74no—
427C2×C4⋊C4—74no—
428C2×C4⋊C4—74no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—74no—
431C2×C4⋊C4—74no—
432C2×C4⋊C4—74no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—144no—
435C2×C4⋊C4—144no—
436C2×C4⋊C4—144no—
437C2×C4⋊C4—144no—
438C2×C4⋊C4—144no—
439C2×C4⋊C4—144no—
440C2×C4⋊C4—282no—
441C2×C4⋊C4—282no—
442C2×C4⋊C4—282no—
443C2×C4⋊C4C22×D714yes—
444C2×C4⋊C4C22×D714yes—
445C2×C4⋊C4C22×D714yes—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—78no—
450C2×C22⋊C4—74no—
451C2×C22⋊C4—74no—
452C2×C22⋊C4—74no—
453C2×C22⋊C4—144no—
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—74no—
462C2×C42—144no—
463C2×C42—144no—
464C2×C42—144no—
465C2×C42—144no—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
470#95—74no—
471#95—74no—
472#95—74no—
473#95—74no—
474#95—74no—
475#95C22×D714yes—
476C22×C7—24no—
477C22×C7—24no—
478C22×C7—24no—
479C22×C7—42no—
480C22×C7—416no—
481C22×C7—42no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7C2×#12314yes—
485C22×C7#53314yes—
486C22×C7#54214yes—
487C22×C7D4×Q814yes—
488C22×C7#55014yes—
489C22×C7#55214yes—
490C22×C7#55414yes—
491C22×C7C23×D411yescharacteristic
492C22×C7C23×Q811yescharacteristic
493C22×C7C22×#4111yescharacteristic
494C22×C7C22×#4111yescharacteristic
495C22×C7C22×#4111yescharacteristic
496C22×C7C2×H(5,𝔽2)11yescharacteristic
497C22×C7C2×2−1+411yescharacteristic
498C4×C7—24no—
499C4×C7—24no—
500C4×C7—42no—
501C4×C7—42no—
502C4×C7—42no—
503C4×C7—42no—
504Dic7—24no—
505Dic7—24no—
506Dic7—24no—
507Dic7—42no—
508Dic7—42no—
509Dic7—42no—
510Dic7—42no—
511Dic7C2×#12318yes—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24Q8×D714yes—
519C24C23×D712yes—
520C24C23×D711yescharacteristic
521C2×Q8—716no—
522C2×Q8—1432no—
523C2×Q8—148no—
524C2×Q8—148no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—74no—
542C22×C4—74no—
543C22×C4—74no—
544C22×C4—72no—
545C22×C4—74no—
546C22×C4—74no—
547C22×C4—74no—
548C22×C4—72no—
549C22×C4—72no—
550C22×C4—72no—
551C22×C4—72no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—148no—
556C22×C4—148no—
557C22×C4—148no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
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—2816no—
577C22×C4D4×D714yes—
578C22×C4#115914yes—
579C22×C4C23×D712yes—
580C22×C4C23×D712yes—
581C22×C4C23×D712yes—
582C22×C4C23×D712yes—
583C22×C4C23×D712yes—
584C22×C4C23×D712yes—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—44no—
588C4⋊C4—148no—
589C4⋊C4—148no—
590C4⋊C4—148no—
591C4⋊C4—148no—
592C4⋊C4—148no—
593C4⋊C4—148no—
594C4⋊C4—148no—
595C4⋊C4—284no—
596C4⋊C4—284no—
597C4⋊C4—284no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—44no—
601C22⋊C4—716no—
602C22⋊C4—148no—
603C22⋊C4—284no—
604C42—148no—
605C42—148no—
606C42—148no—
607C42—148no—
608C2×C7—44no—
609C2×C7#242318yescomplemented
610C2×C7C22×#12311yescharacteristic
611C2×C7C2×#53311yescharacteristic
612C2×C7C2×#54211yescharacteristic
613C2×C7C2×D4×Q811yescharacteristic
614C2×C7C2×#55011yescharacteristic
615C2×C7C2×#55211yescharacteristic
616C2×C7C2×#55411yescharacteristic
617C23—28no—
618C23—28no—
619C23—28no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23C2×D4×D712yes—
631C23C2×#115912yes—
632C23#654812yes—
633C23C2×Q8×D714yes—
634C23C2×Q8×D712yes—
635C23D7×#4112yes—
636C23D7×#4112yes—
637C23#655412yes—
638C23C24×D711yescharacteristic
639Q8—1432no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—716no—
663C2×C4—74no—
664C2×C4—74no—
665C2×C4—74no—
666C2×C4—74no—
667C2×C4—74no—
668C2×C4—74no—
669C2×C4—148no—
670C2×C4—148no—
671C2×C4—148no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—2816no—
691C2×C4—284no—
692C2×C4—284no—
693C2×C4—284no—
694C2×C4—284no—
695C2×C4C2×D4×D714yes—
696C2×C4C2×#115914yes—
697C7C2×#242311yescharacteristic, complemented, Sylow
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—416no—
706C22#9031314yes—
707C22#9032314yes—
708C22#9032714yes—
709C22#9034114yes—
710C22D7×#12314yes—
711C22#9035314yes—
712C22#9040914yes—
713C22C22×D4×D711yescharacteristic
714C22C22×#115911yescharacteristic
715C22C2×#654811yescharacteristic
716C22C22×Q8×D711yescharacteristic
717C22C2×D7×#4111yescharacteristic
718C22C2×D7×#4111yescharacteristic
719C22C2×#655411yescharacteristic
720C4—24no—
721C4—24no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—78no—
727C4—144no—
728C4—144no—
729C4—144no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4—282no—
734C2—44no—
735C2#1173546518yesdirect product factor
736C2C2×#9031311yescharacteristic
737C2C2×#9032311yescharacteristic
738C2C2×#9032711yescharacteristic
739C2C2×#9035311yescharacteristic
740C2C2×#9034111yescharacteristic
741C2C2×D7×#12311yescharacteristic
742C2C2×#9040911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#399C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#399D7
hypocenterC7C2×#2423
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#6450C2semidirect
4. C2×#89752C2semidirect
5. C2×#89756C2semidirect
6. C2×#89744C2semidirect
7. C2×#89753C2semidirect
8. C2×#89748C2semidirect
14. #11735465C2direct (N × H)
15. C2×#89418C2semidirect
16. C2×#89425C2semidirect
43. C2×#6450C22semidirect
57. #89756C22semidirect
58. #89753C22semidirect
59. #89752C22semidirect
60. #89748C22semidirect
61. #89744C22semidirect
67. #89425C22semidirect
68. #89418C22semidirect
107. C2×C22⋊Dic7Q8semidirect
248. C22⋊Dic7C2×Q8semidirect
609. C2×C7#2423semidirect
697. C7C2×#2423semidirect
735. C2#11735465direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64502
C22×#64412
C2×C7×#3992
C2×#897522
C2×#897562
C2×#897442
C2×#897532
C2×#897482
C2×#897212
C2×#897172
C2×#897162
C2×#897142
C2×C22⋊C4×Dic72
#117354652
C2×#894182
C2×#894252
C2×#24237